Álgebra Exemplos

$f (x) = \sqrt[7]{8 x} + 5$

Etapa 1

Escreva $f (x) = \sqrt[7]{8 x} + 5$ como uma equação.

$y = \sqrt[7]{8 x} + 5$

Etapa 2

Alterne as variáveis.

$x = \sqrt[7]{8 y} + 5$

Etapa 3

Resolva $y$ .

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Etapa 3.1

Reescreva a equação como $\sqrt[7]{8 y} + 5 = x$ .

$\sqrt[7]{8 y} + 5 = x$

Etapa 3.2

Subtraia $5$ dos dois lados da equação.

$\sqrt[7]{8 y} = x - 5$

Etapa 3.3

Para remover o radical no lado esquerdo da equação, eleve os dois lados da equação à $7$ ª potência.

${\sqrt[7]{8 y}}^{7} = {(x - 5)}^{7}$

Etapa 3.4

Simplifique cada lado da equação.

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Etapa 3.4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ para reescrever $\sqrt[7]{8 y}$ como ${(8 y)}^{\frac{1}{7}}$ .

${({(8 y)}^{\frac{1}{7}})}^{7} = {(x - 5)}^{7}$

Etapa 3.4.2

Simplifique o lado esquerdo.

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Etapa 3.4.2.1

Simplifique ${({(8 y)}^{\frac{1}{7}})}^{7}$ .

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Etapa 3.4.2.1.1

Multiplique os expoentes em ${({(8 y)}^{\frac{1}{7}})}^{7}$ .

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Etapa 3.4.2.1.1.1

Aplique a regra da multiplicação de potências e multiplique os expoentes, ${(a^{m})}^{n} = a^{m n}$ .

${(8 y)}^{\frac{1}{7} \cdot 7} = {(x - 5)}^{7}$

Etapa 3.4.2.1.1.2

Cancele o fator comum de $7$ .

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Etapa 3.4.2.1.1.2.1

Cancele o fator comum.

${(8 y)}^{\frac{1}{7} \cdot 7} = {(x - 5)}^{7}$

Etapa 3.4.2.1.1.2.2

Reescreva a expressão.

${(8 y)}^{1} = {(x - 5)}^{7}$

Etapa 3.4.2.1.2

Simplifique.

$8 y = {(x - 5)}^{7}$

Etapa 3.4.3

Simplifique o lado direito.

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Etapa 3.4.3.1

Simplifique ${(x - 5)}^{7}$ .

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Etapa 3.4.3.1.1

Use o teorema binomial.

$8 y = x^{7} + 7 x^{6} \cdot - 5 + 21 x^{5} {(- 5)}^{2} + 35 x^{4} {(- 5)}^{3} + 35 x^{3} {(- 5)}^{4} + 21 x^{2} {(- 5)}^{5} + 7 x {(- 5)}^{6} + {(- 5)}^{7}$

Etapa 3.4.3.1.2

Simplifique cada termo.

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Etapa 3.4.3.1.2.1

Multiplique $- 5$ por $7$ .

$8 y = x^{7} - 35 x^{6} + 21 x^{5} {(- 5)}^{2} + 35 x^{4} {(- 5)}^{3} + 35 x^{3} {(- 5)}^{4} + 21 x^{2} {(- 5)}^{5} + 7 x {(- 5)}^{6} + {(- 5)}^{7}$

Etapa 3.4.3.1.2.2

Eleve $- 5$ à potência de $2$ .

$8 y = x^{7} - 35 x^{6} + 21 x^{5} \cdot 25 + 35 x^{4} {(- 5)}^{3} + 35 x^{3} {(- 5)}^{4} + 21 x^{2} {(- 5)}^{5} + 7 x {(- 5)}^{6} + {(- 5)}^{7}$

Etapa 3.4.3.1.2.3

Multiplique $25$ por $21$ .

$8 y = x^{7} - 35 x^{6} + 525 x^{5} + 35 x^{4} {(- 5)}^{3} + 35 x^{3} {(- 5)}^{4} + 21 x^{2} {(- 5)}^{5} + 7 x {(- 5)}^{6} + {(- 5)}^{7}$

Etapa 3.4.3.1.2.4

Eleve $- 5$ à potência de $3$ .

$8 y = x^{7} - 35 x^{6} + 525 x^{5} + 35 x^{4} \cdot - 125 + 35 x^{3} {(- 5)}^{4} + 21 x^{2} {(- 5)}^{5} + 7 x {(- 5)}^{6} + {(- 5)}^{7}$

Etapa 3.4.3.1.2.5

Multiplique $- 125$ por $35$ .

$8 y = x^{7} - 35 x^{6} + 525 x^{5} - 4375 x^{4} + 35 x^{3} {(- 5)}^{4} + 21 x^{2} {(- 5)}^{5} + 7 x {(- 5)}^{6} + {(- 5)}^{7}$

Etapa 3.4.3.1.2.6

Eleve $- 5$ à potência de $4$ .

$8 y = x^{7} - 35 x^{6} + 525 x^{5} - 4375 x^{4} + 35 x^{3} \cdot 625 + 21 x^{2} {(- 5)}^{5} + 7 x {(- 5)}^{6} + {(- 5)}^{7}$

Etapa 3.4.3.1.2.7

Multiplique $625$ por $35$ .

$8 y = x^{7} - 35 x^{6} + 525 x^{5} - 4375 x^{4} + 21875 x^{3} + 21 x^{2} {(- 5)}^{5} + 7 x {(- 5)}^{6} + {(- 5)}^{7}$

Etapa 3.4.3.1.2.8

Eleve $- 5$ à potência de $5$ .

$8 y = x^{7} - 35 x^{6} + 525 x^{5} - 4375 x^{4} + 21875 x^{3} + 21 x^{2} \cdot - 3125 + 7 x {(- 5)}^{6} + {(- 5)}^{7}$

Etapa 3.4.3.1.2.9

Multiplique $- 3125$ por $21$ .

$8 y = x^{7} - 35 x^{6} + 525 x^{5} - 4375 x^{4} + 21875 x^{3} - 65625 x^{2} + 7 x {(- 5)}^{6} + {(- 5)}^{7}$

Etapa 3.4.3.1.2.10

Eleve $- 5$ à potência de $6$ .

$8 y = x^{7} - 35 x^{6} + 525 x^{5} - 4375 x^{4} + 21875 x^{3} - 65625 x^{2} + 7 x \cdot 15625 + {(- 5)}^{7}$

Etapa 3.4.3.1.2.11

Multiplique $15625$ por $7$ .

$8 y = x^{7} - 35 x^{6} + 525 x^{5} - 4375 x^{4} + 21875 x^{3} - 65625 x^{2} + 109375 x + {(- 5)}^{7}$

Etapa 3.4.3.1.2.12

Eleve $- 5$ à potência de $7$ .

$8 y = x^{7} - 35 x^{6} + 525 x^{5} - 4375 x^{4} + 21875 x^{3} - 65625 x^{2} + 109375 x - 78125$

Etapa 3.5

Divida cada termo em $8 y = x^{7} - 35 x^{6} + 525 x^{5} - 4375 x^{4} + 21875 x^{3} - 65625 x^{2} + 109375 x - 78125$ por $8$ e simplifique.

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Etapa 3.5.1

Divida cada termo em $8 y = x^{7} - 35 x^{6} + 525 x^{5} - 4375 x^{4} + 21875 x^{3} - 65625 x^{2} + 109375 x - 78125$ por $8$ .

$\frac{8 y}{8} = \frac{x^{7}}{8} + \frac{- 35 x^{6}}{8} + \frac{525 x^{5}}{8} + \frac{- 4375 x^{4}}{8} + \frac{21875 x^{3}}{8} + \frac{- 65625 x^{2}}{8} + \frac{109375 x}{8} + \frac{- 78125}{8}$

Etapa 3.5.2

Simplifique o lado esquerdo.

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Etapa 3.5.2.1

Cancele o fator comum de $8$ .

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Etapa 3.5.2.1.1

Cancele o fator comum.

$\frac{8 y}{8} = \frac{x^{7}}{8} + \frac{- 35 x^{6}}{8} + \frac{525 x^{5}}{8} + \frac{- 4375 x^{4}}{8} + \frac{21875 x^{3}}{8} + \frac{- 65625 x^{2}}{8} + \frac{109375 x}{8} + \frac{- 78125}{8}$

Etapa 3.5.2.1.2

Divida $y$ por $1$ .

$y = \frac{x^{7}}{8} + \frac{- 35 x^{6}}{8} + \frac{525 x^{5}}{8} + \frac{- 4375 x^{4}}{8} + \frac{21875 x^{3}}{8} + \frac{- 65625 x^{2}}{8} + \frac{109375 x}{8} + \frac{- 78125}{8}$

Etapa 3.5.3

Simplifique o lado direito.

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Etapa 3.5.3.1

Simplifique cada termo.

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Etapa 3.5.3.1.1

Mova o número negativo para a frente da fração.

$y = \frac{x^{7}}{8} - \frac{(35) x^{6}}{8} + \frac{525 x^{5}}{8} + \frac{- 4375 x^{4}}{8} + \frac{21875 x^{3}}{8} + \frac{- 65625 x^{2}}{8} + \frac{109375 x}{8} + \frac{- 78125}{8}$

Etapa 3.5.3.1.2

Mova o número negativo para a frente da fração.

$y = \frac{x^{7}}{8} - \frac{35 x^{6}}{8} + \frac{525 x^{5}}{8} - \frac{(4375) x^{4}}{8} + \frac{21875 x^{3}}{8} + \frac{- 65625 x^{2}}{8} + \frac{109375 x}{8} + \frac{- 78125}{8}$

Etapa 3.5.3.1.3

Mova o número negativo para a frente da fração.

$y = \frac{x^{7}}{8} - \frac{35 x^{6}}{8} + \frac{525 x^{5}}{8} - \frac{4375 x^{4}}{8} + \frac{21875 x^{3}}{8} - \frac{(65625) x^{2}}{8} + \frac{109375 x}{8} + \frac{- 78125}{8}$

Etapa 3.5.3.1.4

Mova o número negativo para a frente da fração.

$y = \frac{x^{7}}{8} - \frac{35 x^{6}}{8} + \frac{525 x^{5}}{8} - \frac{4375 x^{4}}{8} + \frac{21875 x^{3}}{8} - \frac{65625 x^{2}}{8} + \frac{109375 x}{8} - \frac{78125}{8}$

Etapa 4

Replace $y$ with $f^{- 1} (x)$ to show the final answer.

$f^{- 1} (x) = \frac{x^{7}}{8} - \frac{35 x^{6}}{8} + \frac{525 x^{5}}{8} - \frac{4375 x^{4}}{8} + \frac{21875 x^{3}}{8} - \frac{65625 x^{2}}{8} + \frac{109375 x}{8} - \frac{78125}{8}$

Etapa 5

Verifique se $f^{- 1} (x) = \frac{x^{7}}{8} - \frac{35 x^{6}}{8} + \frac{525 x^{5}}{8} - \frac{4375 x^{4}}{8} + \frac{21875 x^{3}}{8} - \frac{65625 x^{2}}{8} + \frac{109375 x}{8} - \frac{78125}{8}$ é o inverso de $f (x) = \sqrt[7]{8 x} + 5$ .

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Etapa 5.1

Para verificar o inverso, veja se $f^{- 1} (f (x)) = x$ e $f (f^{- 1} (x)) = x$ .

Etapa 5.2

Avalie $f^{- 1} (f (x))$ .

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Etapa 5.2.1

Estabeleça a função do resultado composto.

$f^{- 1} (f (x))$

Etapa 5.2.2

Avalie $f^{- 1} (\sqrt[7]{8 x} + 5)$ substituindo o valor de $f$ em $f^{- 1}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{{(\sqrt[7]{8 x} + 5)}^{7}}{8} - \frac{35 {(\sqrt[7]{8 x} + 5)}^{6}}{8} + \frac{525 {(\sqrt[7]{8 x} + 5)}^{5}}{8} - \frac{4375 {(\sqrt[7]{8 x} + 5)}^{4}}{8} + \frac{21875 {(\sqrt[7]{8 x} + 5)}^{3}}{8} - \frac{65625 {(\sqrt[7]{8 x} + 5)}^{2}}{8} + \frac{109375 (\sqrt[7]{8 x} + 5)}{8} - \frac{78125}{8}$

Etapa 5.2.3

Combine os numeradores em relação ao denominador comum.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{{(\sqrt[7]{8 x} + 5)}^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4

Simplifique cada termo.

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Etapa 5.2.4.1

Use o teorema binomial.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{{\sqrt[7]{8 x}}^{7} + 7 {\sqrt[7]{8 x}}^{6} \cdot 5 + 21 {\sqrt[7]{8 x}}^{5} \cdot 5^{2} + 35 {\sqrt[7]{8 x}}^{4} \cdot 5^{3} + 35 {\sqrt[7]{8 x}}^{3} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2

Simplifique cada termo.

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Etapa 5.2.4.2.1

Reescreva ${\sqrt[7]{8 x}}^{7}$ como $8 x$ .

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Etapa 5.2.4.2.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ para reescrever $\sqrt[7]{8 x}$ como ${(8 x)}^{\frac{1}{7}}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{{({(8 x)}^{\frac{1}{7}})}^{7} + 7 {\sqrt[7]{8 x}}^{6} \cdot 5 + 21 {\sqrt[7]{8 x}}^{5} \cdot 5^{2} + 35 {\sqrt[7]{8 x}}^{4} \cdot 5^{3} + 35 {\sqrt[7]{8 x}}^{3} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.1.2

Aplique a regra da multiplicação de potências e multiplique os expoentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{{(8 x)}^{\frac{1}{7} \cdot 7} + 7 {\sqrt[7]{8 x}}^{6} \cdot 5 + 21 {\sqrt[7]{8 x}}^{5} \cdot 5^{2} + 35 {\sqrt[7]{8 x}}^{4} \cdot 5^{3} + 35 {\sqrt[7]{8 x}}^{3} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.1.3

Combine $\frac{1}{7}$ e $7$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{{(8 x)}^{\frac{7}{7}} + 7 {\sqrt[7]{8 x}}^{6} \cdot 5 + 21 {\sqrt[7]{8 x}}^{5} \cdot 5^{2} + 35 {\sqrt[7]{8 x}}^{4} \cdot 5^{3} + 35 {\sqrt[7]{8 x}}^{3} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.1.4

Cancele o fator comum de $7$ .

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Etapa 5.2.4.2.1.4.1

Cancele o fator comum.

Etapa 5.2.4.2.1.4.2

Reescreva a expressão.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{(8 x) + 7 {\sqrt[7]{8 x}}^{6} \cdot 5 + 21 {\sqrt[7]{8 x}}^{5} \cdot 5^{2} + 35 {\sqrt[7]{8 x}}^{4} \cdot 5^{3} + 35 {\sqrt[7]{8 x}}^{3} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.1.5

Simplifique.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 7 {\sqrt[7]{8 x}}^{6} \cdot 5 + 21 {\sqrt[7]{8 x}}^{5} \cdot 5^{2} + 35 {\sqrt[7]{8 x}}^{4} \cdot 5^{3} + 35 {\sqrt[7]{8 x}}^{3} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.2

Reescreva ${\sqrt[7]{8 x}}^{6}$ como $\sqrt[7]{{(8 x)}^{6}}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 7 \sqrt[7]{{(8 x)}^{6}} \cdot 5 + 21 {\sqrt[7]{8 x}}^{5} \cdot 5^{2} + 35 {\sqrt[7]{8 x}}^{4} \cdot 5^{3} + 35 {\sqrt[7]{8 x}}^{3} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.3

Aplique a regra do produto a $8 x$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 7 \sqrt[7]{8^{6} x^{6}} \cdot 5 + 21 {\sqrt[7]{8 x}}^{5} \cdot 5^{2} + 35 {\sqrt[7]{8 x}}^{4} \cdot 5^{3} + 35 {\sqrt[7]{8 x}}^{3} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.4

Eleve $8$ à potência de $6$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 7 \sqrt[7]{262144 x^{6}} \cdot 5 + 21 {\sqrt[7]{8 x}}^{5} \cdot 5^{2} + 35 {\sqrt[7]{8 x}}^{4} \cdot 5^{3} + 35 {\sqrt[7]{8 x}}^{3} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.5

Reescreva $262144 x^{6}$ como $4^{7} \cdot (16 x^{6})$ .

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Etapa 5.2.4.2.5.1

Fatore $16384$ de $262144$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 7 \sqrt[7]{16384 (16) x^{6}} \cdot 5 + 21 {\sqrt[7]{8 x}}^{5} \cdot 5^{2} + 35 {\sqrt[7]{8 x}}^{4} \cdot 5^{3} + 35 {\sqrt[7]{8 x}}^{3} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.5.2

Reescreva $16384$ como $4^{7}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 7 \sqrt[7]{4^{7} \cdot (16 x^{6})} \cdot 5 + 21 {\sqrt[7]{8 x}}^{5} \cdot 5^{2} + 35 {\sqrt[7]{8 x}}^{4} \cdot 5^{3} + 35 {\sqrt[7]{8 x}}^{3} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.5.3

Adicione parênteses.

Etapa 5.2.4.2.6

Elimine os termos abaixo do radical.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 7 (4 \sqrt[7]{16 x^{6}}) \cdot 5 + 21 {\sqrt[7]{8 x}}^{5} \cdot 5^{2} + 35 {\sqrt[7]{8 x}}^{4} \cdot 5^{3} + 35 {\sqrt[7]{8 x}}^{3} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.7

Multiplique $4$ por $7$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 28 \sqrt[7]{16 x^{6}} \cdot 5 + 21 {\sqrt[7]{8 x}}^{5} \cdot 5^{2} + 35 {\sqrt[7]{8 x}}^{4} \cdot 5^{3} + 35 {\sqrt[7]{8 x}}^{3} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.8

Multiplique $5$ por $28$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 21 {\sqrt[7]{8 x}}^{5} \cdot 5^{2} + 35 {\sqrt[7]{8 x}}^{4} \cdot 5^{3} + 35 {\sqrt[7]{8 x}}^{3} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.9

Reescreva ${\sqrt[7]{8 x}}^{5}$ como $\sqrt[7]{{(8 x)}^{5}}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 21 \sqrt[7]{{(8 x)}^{5}} \cdot 5^{2} + 35 {\sqrt[7]{8 x}}^{4} \cdot 5^{3} + 35 {\sqrt[7]{8 x}}^{3} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.10

Aplique a regra do produto a $8 x$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 21 \sqrt[7]{8^{5} x^{5}} \cdot 5^{2} + 35 {\sqrt[7]{8 x}}^{4} \cdot 5^{3} + 35 {\sqrt[7]{8 x}}^{3} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.11

Eleve $8$ à potência de $5$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 21 \sqrt[7]{32768 x^{5}} \cdot 5^{2} + 35 {\sqrt[7]{8 x}}^{4} \cdot 5^{3} + 35 {\sqrt[7]{8 x}}^{3} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.12

Reescreva $32768 x^{5}$ como $4^{7} \cdot (2 x^{5})$ .

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Etapa 5.2.4.2.12.1

Fatore $16384$ de $32768$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 21 \sqrt[7]{16384 (2) x^{5}} \cdot 5^{2} + 35 {\sqrt[7]{8 x}}^{4} \cdot 5^{3} + 35 {\sqrt[7]{8 x}}^{3} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.12.2

Reescreva $16384$ como $4^{7}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 21 \sqrt[7]{4^{7} \cdot (2 x^{5})} \cdot 5^{2} + 35 {\sqrt[7]{8 x}}^{4} \cdot 5^{3} + 35 {\sqrt[7]{8 x}}^{3} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.12.3

Adicione parênteses.

Etapa 5.2.4.2.13

Elimine os termos abaixo do radical.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 21 (4 \sqrt[7]{2 x^{5}}) \cdot 5^{2} + 35 {\sqrt[7]{8 x}}^{4} \cdot 5^{3} + 35 {\sqrt[7]{8 x}}^{3} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.14

Multiplique $4$ por $21$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 84 \sqrt[7]{2 x^{5}} \cdot 5^{2} + 35 {\sqrt[7]{8 x}}^{4} \cdot 5^{3} + 35 {\sqrt[7]{8 x}}^{3} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.15

Eleve $5$ à potência de $2$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 84 \sqrt[7]{2 x^{5}} \cdot 25 + 35 {\sqrt[7]{8 x}}^{4} \cdot 5^{3} + 35 {\sqrt[7]{8 x}}^{3} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.16

Multiplique $25$ por $84$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 35 {\sqrt[7]{8 x}}^{4} \cdot 5^{3} + 35 {\sqrt[7]{8 x}}^{3} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.17

Reescreva ${\sqrt[7]{8 x}}^{4}$ como $\sqrt[7]{{(8 x)}^{4}}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 35 \sqrt[7]{{(8 x)}^{4}} \cdot 5^{3} + 35 {\sqrt[7]{8 x}}^{3} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.18

Aplique a regra do produto a $8 x$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 35 \sqrt[7]{8^{4} x^{4}} \cdot 5^{3} + 35 {\sqrt[7]{8 x}}^{3} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.19

Eleve $8$ à potência de $4$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 35 \sqrt[7]{4096 x^{4}} \cdot 5^{3} + 35 {\sqrt[7]{8 x}}^{3} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.20

Reescreva $4096 x^{4}$ como $2^{7} \cdot (32 x^{4})$ .

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Etapa 5.2.4.2.20.1

Fatore $128$ de $4096$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 35 \sqrt[7]{128 (32) x^{4}} \cdot 5^{3} + 35 {\sqrt[7]{8 x}}^{3} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.20.2

Reescreva $128$ como $2^{7}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 35 \sqrt[7]{2^{7} \cdot (32 x^{4})} \cdot 5^{3} + 35 {\sqrt[7]{8 x}}^{3} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.20.3

Adicione parênteses.

Etapa 5.2.4.2.21

Elimine os termos abaixo do radical.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 35 (2 \sqrt[7]{32 x^{4}}) \cdot 5^{3} + 35 {\sqrt[7]{8 x}}^{3} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.22

Multiplique $2$ por $35$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 70 \sqrt[7]{32 x^{4}} \cdot 5^{3} + 35 {\sqrt[7]{8 x}}^{3} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.23

Eleve $5$ à potência de $3$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 70 \sqrt[7]{32 x^{4}} \cdot 125 + 35 {\sqrt[7]{8 x}}^{3} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.24

Multiplique $125$ por $70$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 35 {\sqrt[7]{8 x}}^{3} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.25

Reescreva ${\sqrt[7]{8 x}}^{3}$ como $\sqrt[7]{{(8 x)}^{3}}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 35 \sqrt[7]{{(8 x)}^{3}} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.26

Aplique a regra do produto a $8 x$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 35 \sqrt[7]{8^{3} x^{3}} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.27

Eleve $8$ à potência de $3$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 35 \sqrt[7]{512 x^{3}} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.28

Reescreva $512 x^{3}$ como $2^{7} \cdot (4 x^{3})$ .

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Etapa 5.2.4.2.28.1

Fatore $128$ de $512$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 35 \sqrt[7]{128 (4) x^{3}} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.28.2

Reescreva $128$ como $2^{7}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 35 \sqrt[7]{2^{7} \cdot (4 x^{3})} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.28.3

Adicione parênteses.

Etapa 5.2.4.2.29

Elimine os termos abaixo do radical.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 35 (2 \sqrt[7]{4 x^{3}}) \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.30

Multiplique $2$ por $35$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 70 \sqrt[7]{4 x^{3}} \cdot 5^{4} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.31

Eleve $5$ à potência de $4$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 70 \sqrt[7]{4 x^{3}} \cdot 625 + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.32

Multiplique $625$ por $70$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 21 {\sqrt[7]{8 x}}^{2} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.33

Reescreva ${\sqrt[7]{8 x}}^{2}$ como $\sqrt[7]{{(8 x)}^{2}}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 21 \sqrt[7]{{(8 x)}^{2}} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.34

Aplique a regra do produto a $8 x$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 21 \sqrt[7]{8^{2} x^{2}} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.35

Eleve $8$ à potência de $2$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 21 \sqrt[7]{64 x^{2}} \cdot 5^{5} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.36

Eleve $5$ à potência de $5$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 21 \sqrt[7]{64 x^{2}} \cdot 3125 + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.37

Multiplique $3125$ por $21$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 7 \sqrt[7]{8 x} \cdot 5^{6} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.38

Eleve $5$ à potência de $6$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 7 \sqrt[7]{8 x} \cdot 15625 + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.39

Multiplique $15625$ por $7$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 5^{7} - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.2.40

Eleve $5$ à potência de $7$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 35 {(\sqrt[7]{8 x} + 5)}^{6} + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.3

Use o teorema binomial.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 35 ({\sqrt[7]{8 x}}^{6} + 6 {\sqrt[7]{8 x}}^{5} \cdot 5 + 15 {\sqrt[7]{8 x}}^{4} \cdot 5^{2} + 20 {\sqrt[7]{8 x}}^{3} \cdot 5^{3} + 15 {\sqrt[7]{8 x}}^{2} \cdot 5^{4} + 6 \sqrt[7]{8 x} \cdot 5^{5} + 5^{6}) + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.4

Simplifique cada termo.

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Etapa 5.2.4.4.1

Reescreva ${\sqrt[7]{8 x}}^{6}$ como $\sqrt[7]{{(8 x)}^{6}}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 35 (\sqrt[7]{{(8 x)}^{6}} + 6 {\sqrt[7]{8 x}}^{5} \cdot 5 + 15 {\sqrt[7]{8 x}}^{4} \cdot 5^{2} + 20 {\sqrt[7]{8 x}}^{3} \cdot 5^{3} + 15 {\sqrt[7]{8 x}}^{2} \cdot 5^{4} + 6 \sqrt[7]{8 x} \cdot 5^{5} + 5^{6}) + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.4.2

Aplique a regra do produto a $8 x$ .

Etapa 5.2.4.4.3

Eleve $8$ à potência de $6$ .

Etapa 5.2.4.4.4

Reescreva $262144 x^{6}$ como $4^{7} \cdot (16 x^{6})$ .

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Etapa 5.2.4.4.4.1

Fatore $16384$ de $262144$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 35 (\sqrt[7]{16384 (16) x^{6}} + 6 {\sqrt[7]{8 x}}^{5} \cdot 5 + 15 {\sqrt[7]{8 x}}^{4} \cdot 5^{2} + 20 {\sqrt[7]{8 x}}^{3} \cdot 5^{3} + 15 {\sqrt[7]{8 x}}^{2} \cdot 5^{4} + 6 \sqrt[7]{8 x} \cdot 5^{5} + 5^{6}) + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.4.4.2

Reescreva $16384$ como $4^{7}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 35 (\sqrt[7]{4^{7} \cdot (16 x^{6})} + 6 {\sqrt[7]{8 x}}^{5} \cdot 5 + 15 {\sqrt[7]{8 x}}^{4} \cdot 5^{2} + 20 {\sqrt[7]{8 x}}^{3} \cdot 5^{3} + 15 {\sqrt[7]{8 x}}^{2} \cdot 5^{4} + 6 \sqrt[7]{8 x} \cdot 5^{5} + 5^{6}) + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.4.4.3

Adicione parênteses.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 35 (\sqrt[7]{4^{7} \cdot (16 x^{6})} + 6 {\sqrt[7]{8 x}}^{5} \cdot 5 + 15 {\sqrt[7]{8 x}}^{4} \cdot 5^{2} + 20 {\sqrt[7]{8 x}}^{3} \cdot 5^{3} + 15 {\sqrt[7]{8 x}}^{2} \cdot 5^{4} + 6 \sqrt[7]{8 x} \cdot 5^{5} + 5^{6}) + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.4.5

Elimine os termos abaixo do radical.

Etapa 5.2.4.4.6

Reescreva ${\sqrt[7]{8 x}}^{5}$ como $\sqrt[7]{{(8 x)}^{5}}$ .

Etapa 5.2.4.4.7

Aplique a regra do produto a $8 x$ .

Etapa 5.2.4.4.8

Eleve $8$ à potência de $5$ .

Etapa 5.2.4.4.9

Reescreva $32768 x^{5}$ como $4^{7} \cdot (2 x^{5})$ .

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Etapa 5.2.4.4.9.1

Fatore $16384$ de $32768$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 35 (4 \sqrt[7]{16 x^{6}} + 6 \sqrt[7]{16384 (2) x^{5}} \cdot 5 + 15 {\sqrt[7]{8 x}}^{4} \cdot 5^{2} + 20 {\sqrt[7]{8 x}}^{3} \cdot 5^{3} + 15 {\sqrt[7]{8 x}}^{2} \cdot 5^{4} + 6 \sqrt[7]{8 x} \cdot 5^{5} + 5^{6}) + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.4.9.2

Reescreva $16384$ como $4^{7}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 35 (4 \sqrt[7]{16 x^{6}} + 6 \sqrt[7]{4^{7} \cdot (2 x^{5})} \cdot 5 + 15 {\sqrt[7]{8 x}}^{4} \cdot 5^{2} + 20 {\sqrt[7]{8 x}}^{3} \cdot 5^{3} + 15 {\sqrt[7]{8 x}}^{2} \cdot 5^{4} + 6 \sqrt[7]{8 x} \cdot 5^{5} + 5^{6}) + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.4.9.3

Adicione parênteses.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 35 (4 \sqrt[7]{16 x^{6}} + 6 \sqrt[7]{4^{7} \cdot (2 x^{5})} \cdot 5 + 15 {\sqrt[7]{8 x}}^{4} \cdot 5^{2} + 20 {\sqrt[7]{8 x}}^{3} \cdot 5^{3} + 15 {\sqrt[7]{8 x}}^{2} \cdot 5^{4} + 6 \sqrt[7]{8 x} \cdot 5^{5} + 5^{6}) + 525 {(\sqrt[7]{8 x} + 5)}^{5} - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.4.10

Elimine os termos abaixo do radical.

Etapa 5.2.4.4.11

Multiplique $4$ por $6$ .

Etapa 5.2.4.4.12

Multiplique $5$ por $24$ .

Etapa 5.2.4.4.13

Reescreva ${\sqrt[7]{8 x}}^{4}$ como $\sqrt[7]{{(8 x)}^{4}}$ .

Etapa 5.2.4.4.14

Aplique a regra do produto a $8 x$ .

Etapa 5.2.4.4.15

Eleve $8$ à potência de $4$ .

Etapa 5.2.4.4.16

Reescreva $4096 x^{4}$ como $2^{7} \cdot (32 x^{4})$ .

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Etapa 5.2.4.4.16.1

Fatore $128$ de $4096$ .

Etapa 5.2.4.4.16.2

Reescreva $128$ como $2^{7}$ .

Etapa 5.2.4.4.16.3

Adicione parênteses.

Etapa 5.2.4.4.17

Elimine os termos abaixo do radical.

Etapa 5.2.4.4.18

Multiplique $2$ por $15$ .

Etapa 5.2.4.4.19

Eleve $5$ à potência de $2$ .

Etapa 5.2.4.4.20

Multiplique $25$ por $30$ .

Etapa 5.2.4.4.21

Reescreva ${\sqrt[7]{8 x}}^{3}$ como $\sqrt[7]{{(8 x)}^{3}}$ .

Etapa 5.2.4.4.22

Aplique a regra do produto a $8 x$ .

Etapa 5.2.4.4.23

Eleve $8$ à potência de $3$ .

Etapa 5.2.4.4.24

Reescreva $512 x^{3}$ como $2^{7} \cdot (4 x^{3})$ .

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Etapa 5.2.4.4.24.1

Fatore $128$ de $512$ .

Etapa 5.2.4.4.24.2

Reescreva $128$ como $2^{7}$ .

Etapa 5.2.4.4.24.3

Adicione parênteses.

Etapa 5.2.4.4.25

Elimine os termos abaixo do radical.

Etapa 5.2.4.4.26

Multiplique $2$ por $20$ .

Etapa 5.2.4.4.27

Eleve $5$ à potência de $3$ .

Etapa 5.2.4.4.28

Multiplique $125$ por $40$ .

Etapa 5.2.4.4.29

Reescreva ${\sqrt[7]{8 x}}^{2}$ como $\sqrt[7]{{(8 x)}^{2}}$ .

Etapa 5.2.4.4.30

Aplique a regra do produto a $8 x$ .

Etapa 5.2.4.4.31

Eleve $8$ à potência de $2$ .

Etapa 5.2.4.4.32

Eleve $5$ à potência de $4$ .

Etapa 5.2.4.4.33

Multiplique $625$ por $15$ .

Etapa 5.2.4.4.34

Eleve $5$ à potência de $5$ .

Etapa 5.2.4.4.35

Multiplique $3125$ por $6$ .

Etapa 5.2.4.4.36

Eleve $5$ à potência de $6$ .

Etapa 5.2.4.5

Aplique a propriedade distributiva.

Etapa 5.2.4.6

Simplifique.

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Etapa 5.2.4.6.1

Multiplique $4$ por $- 35$ .

Etapa 5.2.4.6.2

Multiplique $120$ por $- 35$ .

Etapa 5.2.4.6.3

Multiplique $750$ por $- 35$ .

Etapa 5.2.4.6.4

Multiplique $5000$ por $- 35$ .

Etapa 5.2.4.6.5

Multiplique $9375$ por $- 35$ .

Etapa 5.2.4.6.6

Multiplique $18750$ por $- 35$ .

Etapa 5.2.4.6.7

Multiplique $- 35$ por $15625$ .

Etapa 5.2.4.7

Use o teorema binomial.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 ({\sqrt[7]{8 x}}^{5} + 5 {\sqrt[7]{8 x}}^{4} \cdot 5 + 10 {\sqrt[7]{8 x}}^{3} \cdot 5^{2} + 10 {\sqrt[7]{8 x}}^{2} \cdot 5^{3} + 5 \sqrt[7]{8 x} \cdot 5^{4} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8

Simplifique cada termo.

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Etapa 5.2.4.8.1

Reescreva ${\sqrt[7]{8 x}}^{5}$ como $\sqrt[7]{{(8 x)}^{5}}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (\sqrt[7]{{(8 x)}^{5}} + 5 {\sqrt[7]{8 x}}^{4} \cdot 5 + 10 {\sqrt[7]{8 x}}^{3} \cdot 5^{2} + 10 {\sqrt[7]{8 x}}^{2} \cdot 5^{3} + 5 \sqrt[7]{8 x} \cdot 5^{4} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.2

Aplique a regra do produto a $8 x$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (\sqrt[7]{8^{5} x^{5}} + 5 {\sqrt[7]{8 x}}^{4} \cdot 5 + 10 {\sqrt[7]{8 x}}^{3} \cdot 5^{2} + 10 {\sqrt[7]{8 x}}^{2} \cdot 5^{3} + 5 \sqrt[7]{8 x} \cdot 5^{4} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.3

Eleve $8$ à potência de $5$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (\sqrt[7]{32768 x^{5}} + 5 {\sqrt[7]{8 x}}^{4} \cdot 5 + 10 {\sqrt[7]{8 x}}^{3} \cdot 5^{2} + 10 {\sqrt[7]{8 x}}^{2} \cdot 5^{3} + 5 \sqrt[7]{8 x} \cdot 5^{4} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.4

Reescreva $32768 x^{5}$ como $4^{7} \cdot (2 x^{5})$ .

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Etapa 5.2.4.8.4.1

Fatore $16384$ de $32768$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (\sqrt[7]{16384 (2) x^{5}} + 5 {\sqrt[7]{8 x}}^{4} \cdot 5 + 10 {\sqrt[7]{8 x}}^{3} \cdot 5^{2} + 10 {\sqrt[7]{8 x}}^{2} \cdot 5^{3} + 5 \sqrt[7]{8 x} \cdot 5^{4} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.4.2

Reescreva $16384$ como $4^{7}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (\sqrt[7]{4^{7} \cdot (2 x^{5})} + 5 {\sqrt[7]{8 x}}^{4} \cdot 5 + 10 {\sqrt[7]{8 x}}^{3} \cdot 5^{2} + 10 {\sqrt[7]{8 x}}^{2} \cdot 5^{3} + 5 \sqrt[7]{8 x} \cdot 5^{4} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.4.3

Adicione parênteses.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (\sqrt[7]{4^{7} \cdot (2 x^{5})} + 5 {\sqrt[7]{8 x}}^{4} \cdot 5 + 10 {\sqrt[7]{8 x}}^{3} \cdot 5^{2} + 10 {\sqrt[7]{8 x}}^{2} \cdot 5^{3} + 5 \sqrt[7]{8 x} \cdot 5^{4} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.5

Elimine os termos abaixo do radical.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (4 \sqrt[7]{2 x^{5}} + 5 {\sqrt[7]{8 x}}^{4} \cdot 5 + 10 {\sqrt[7]{8 x}}^{3} \cdot 5^{2} + 10 {\sqrt[7]{8 x}}^{2} \cdot 5^{3} + 5 \sqrt[7]{8 x} \cdot 5^{4} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.6

Reescreva ${\sqrt[7]{8 x}}^{4}$ como $\sqrt[7]{{(8 x)}^{4}}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (4 \sqrt[7]{2 x^{5}} + 5 \sqrt[7]{{(8 x)}^{4}} \cdot 5 + 10 {\sqrt[7]{8 x}}^{3} \cdot 5^{2} + 10 {\sqrt[7]{8 x}}^{2} \cdot 5^{3} + 5 \sqrt[7]{8 x} \cdot 5^{4} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.7

Aplique a regra do produto a $8 x$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (4 \sqrt[7]{2 x^{5}} + 5 \sqrt[7]{8^{4} x^{4}} \cdot 5 + 10 {\sqrt[7]{8 x}}^{3} \cdot 5^{2} + 10 {\sqrt[7]{8 x}}^{2} \cdot 5^{3} + 5 \sqrt[7]{8 x} \cdot 5^{4} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.8

Eleve $8$ à potência de $4$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (4 \sqrt[7]{2 x^{5}} + 5 \sqrt[7]{4096 x^{4}} \cdot 5 + 10 {\sqrt[7]{8 x}}^{3} \cdot 5^{2} + 10 {\sqrt[7]{8 x}}^{2} \cdot 5^{3} + 5 \sqrt[7]{8 x} \cdot 5^{4} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.9

Reescreva $4096 x^{4}$ como $2^{7} \cdot (32 x^{4})$ .

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Etapa 5.2.4.8.9.1

Fatore $128$ de $4096$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (4 \sqrt[7]{2 x^{5}} + 5 \sqrt[7]{128 (32) x^{4}} \cdot 5 + 10 {\sqrt[7]{8 x}}^{3} \cdot 5^{2} + 10 {\sqrt[7]{8 x}}^{2} \cdot 5^{3} + 5 \sqrt[7]{8 x} \cdot 5^{4} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.9.2

Reescreva $128$ como $2^{7}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (4 \sqrt[7]{2 x^{5}} + 5 \sqrt[7]{2^{7} \cdot (32 x^{4})} \cdot 5 + 10 {\sqrt[7]{8 x}}^{3} \cdot 5^{2} + 10 {\sqrt[7]{8 x}}^{2} \cdot 5^{3} + 5 \sqrt[7]{8 x} \cdot 5^{4} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.9.3

Adicione parênteses.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (4 \sqrt[7]{2 x^{5}} + 5 \sqrt[7]{2^{7} \cdot (32 x^{4})} \cdot 5 + 10 {\sqrt[7]{8 x}}^{3} \cdot 5^{2} + 10 {\sqrt[7]{8 x}}^{2} \cdot 5^{3} + 5 \sqrt[7]{8 x} \cdot 5^{4} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.10

Elimine os termos abaixo do radical.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (4 \sqrt[7]{2 x^{5}} + 5 (2 \sqrt[7]{32 x^{4}}) \cdot 5 + 10 {\sqrt[7]{8 x}}^{3} \cdot 5^{2} + 10 {\sqrt[7]{8 x}}^{2} \cdot 5^{3} + 5 \sqrt[7]{8 x} \cdot 5^{4} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.11

Multiplique $2$ por $5$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (4 \sqrt[7]{2 x^{5}} + 10 \sqrt[7]{32 x^{4}} \cdot 5 + 10 {\sqrt[7]{8 x}}^{3} \cdot 5^{2} + 10 {\sqrt[7]{8 x}}^{2} \cdot 5^{3} + 5 \sqrt[7]{8 x} \cdot 5^{4} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.12

Multiplique $5$ por $10$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (4 \sqrt[7]{2 x^{5}} + 50 \sqrt[7]{32 x^{4}} + 10 {\sqrt[7]{8 x}}^{3} \cdot 5^{2} + 10 {\sqrt[7]{8 x}}^{2} \cdot 5^{3} + 5 \sqrt[7]{8 x} \cdot 5^{4} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.13

Reescreva ${\sqrt[7]{8 x}}^{3}$ como $\sqrt[7]{{(8 x)}^{3}}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (4 \sqrt[7]{2 x^{5}} + 50 \sqrt[7]{32 x^{4}} + 10 \sqrt[7]{{(8 x)}^{3}} \cdot 5^{2} + 10 {\sqrt[7]{8 x}}^{2} \cdot 5^{3} + 5 \sqrt[7]{8 x} \cdot 5^{4} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.14

Aplique a regra do produto a $8 x$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (4 \sqrt[7]{2 x^{5}} + 50 \sqrt[7]{32 x^{4}} + 10 \sqrt[7]{8^{3} x^{3}} \cdot 5^{2} + 10 {\sqrt[7]{8 x}}^{2} \cdot 5^{3} + 5 \sqrt[7]{8 x} \cdot 5^{4} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.15

Eleve $8$ à potência de $3$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (4 \sqrt[7]{2 x^{5}} + 50 \sqrt[7]{32 x^{4}} + 10 \sqrt[7]{512 x^{3}} \cdot 5^{2} + 10 {\sqrt[7]{8 x}}^{2} \cdot 5^{3} + 5 \sqrt[7]{8 x} \cdot 5^{4} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.16

Reescreva $512 x^{3}$ como $2^{7} \cdot (4 x^{3})$ .

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Etapa 5.2.4.8.16.1

Fatore $128$ de $512$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (4 \sqrt[7]{2 x^{5}} + 50 \sqrt[7]{32 x^{4}} + 10 \sqrt[7]{128 (4) x^{3}} \cdot 5^{2} + 10 {\sqrt[7]{8 x}}^{2} \cdot 5^{3} + 5 \sqrt[7]{8 x} \cdot 5^{4} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.16.2

Reescreva $128$ como $2^{7}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (4 \sqrt[7]{2 x^{5}} + 50 \sqrt[7]{32 x^{4}} + 10 \sqrt[7]{2^{7} \cdot (4 x^{3})} \cdot 5^{2} + 10 {\sqrt[7]{8 x}}^{2} \cdot 5^{3} + 5 \sqrt[7]{8 x} \cdot 5^{4} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.16.3

Adicione parênteses.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (4 \sqrt[7]{2 x^{5}} + 50 \sqrt[7]{32 x^{4}} + 10 \sqrt[7]{2^{7} \cdot (4 x^{3})} \cdot 5^{2} + 10 {\sqrt[7]{8 x}}^{2} \cdot 5^{3} + 5 \sqrt[7]{8 x} \cdot 5^{4} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.17

Elimine os termos abaixo do radical.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (4 \sqrt[7]{2 x^{5}} + 50 \sqrt[7]{32 x^{4}} + 10 (2 \sqrt[7]{4 x^{3}}) \cdot 5^{2} + 10 {\sqrt[7]{8 x}}^{2} \cdot 5^{3} + 5 \sqrt[7]{8 x} \cdot 5^{4} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.18

Multiplique $2$ por $10$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (4 \sqrt[7]{2 x^{5}} + 50 \sqrt[7]{32 x^{4}} + 20 \sqrt[7]{4 x^{3}} \cdot 5^{2} + 10 {\sqrt[7]{8 x}}^{2} \cdot 5^{3} + 5 \sqrt[7]{8 x} \cdot 5^{4} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.19

Eleve $5$ à potência de $2$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (4 \sqrt[7]{2 x^{5}} + 50 \sqrt[7]{32 x^{4}} + 20 \sqrt[7]{4 x^{3}} \cdot 25 + 10 {\sqrt[7]{8 x}}^{2} \cdot 5^{3} + 5 \sqrt[7]{8 x} \cdot 5^{4} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.20

Multiplique $25$ por $20$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (4 \sqrt[7]{2 x^{5}} + 50 \sqrt[7]{32 x^{4}} + 500 \sqrt[7]{4 x^{3}} + 10 {\sqrt[7]{8 x}}^{2} \cdot 5^{3} + 5 \sqrt[7]{8 x} \cdot 5^{4} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.21

Reescreva ${\sqrt[7]{8 x}}^{2}$ como $\sqrt[7]{{(8 x)}^{2}}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (4 \sqrt[7]{2 x^{5}} + 50 \sqrt[7]{32 x^{4}} + 500 \sqrt[7]{4 x^{3}} + 10 \sqrt[7]{{(8 x)}^{2}} \cdot 5^{3} + 5 \sqrt[7]{8 x} \cdot 5^{4} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.22

Aplique a regra do produto a $8 x$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (4 \sqrt[7]{2 x^{5}} + 50 \sqrt[7]{32 x^{4}} + 500 \sqrt[7]{4 x^{3}} + 10 \sqrt[7]{8^{2} x^{2}} \cdot 5^{3} + 5 \sqrt[7]{8 x} \cdot 5^{4} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.23

Eleve $8$ à potência de $2$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (4 \sqrt[7]{2 x^{5}} + 50 \sqrt[7]{32 x^{4}} + 500 \sqrt[7]{4 x^{3}} + 10 \sqrt[7]{64 x^{2}} \cdot 5^{3} + 5 \sqrt[7]{8 x} \cdot 5^{4} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.24

Eleve $5$ à potência de $3$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (4 \sqrt[7]{2 x^{5}} + 50 \sqrt[7]{32 x^{4}} + 500 \sqrt[7]{4 x^{3}} + 10 \sqrt[7]{64 x^{2}} \cdot 125 + 5 \sqrt[7]{8 x} \cdot 5^{4} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.25

Multiplique $125$ por $10$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (4 \sqrt[7]{2 x^{5}} + 50 \sqrt[7]{32 x^{4}} + 500 \sqrt[7]{4 x^{3}} + 1250 \sqrt[7]{64 x^{2}} + 5 \sqrt[7]{8 x} \cdot 5^{4} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.26

Multiplique $5$ por $5^{4}$ somando os expoentes.

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Etapa 5.2.4.8.26.1

Mova $5^{4}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (4 \sqrt[7]{2 x^{5}} + 50 \sqrt[7]{32 x^{4}} + 500 \sqrt[7]{4 x^{3}} + 1250 \sqrt[7]{64 x^{2}} + 5^{4} \cdot (5 \sqrt[7]{8 x}) + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.26.2

Multiplique $5^{4}$ por $5$ .

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Etapa 5.2.4.8.26.2.1

Eleve $5$ à potência de $1$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (4 \sqrt[7]{2 x^{5}} + 50 \sqrt[7]{32 x^{4}} + 500 \sqrt[7]{4 x^{3}} + 1250 \sqrt[7]{64 x^{2}} + 5^{4} \cdot (5 \sqrt[7]{8 x}) + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.26.2.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (4 \sqrt[7]{2 x^{5}} + 50 \sqrt[7]{32 x^{4}} + 500 \sqrt[7]{4 x^{3}} + 1250 \sqrt[7]{64 x^{2}} + 5^{4 + 1} \sqrt[7]{8 x} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.26.3

Some $4$ e $1$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (4 \sqrt[7]{2 x^{5}} + 50 \sqrt[7]{32 x^{4}} + 500 \sqrt[7]{4 x^{3}} + 1250 \sqrt[7]{64 x^{2}} + 5^{5} \sqrt[7]{8 x} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.27

Eleve $5$ à potência de $5$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (4 \sqrt[7]{2 x^{5}} + 50 \sqrt[7]{32 x^{4}} + 500 \sqrt[7]{4 x^{3}} + 1250 \sqrt[7]{64 x^{2}} + 3125 \sqrt[7]{8 x} + 5^{5}) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.8.28

Eleve $5$ à potência de $5$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (4 \sqrt[7]{2 x^{5}} + 50 \sqrt[7]{32 x^{4}} + 500 \sqrt[7]{4 x^{3}} + 1250 \sqrt[7]{64 x^{2}} + 3125 \sqrt[7]{8 x} + 3125) - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.9

Aplique a propriedade distributiva.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 525 (4 \sqrt[7]{2 x^{5}}) + 525 (50 \sqrt[7]{32 x^{4}}) + 525 (500 \sqrt[7]{4 x^{3}}) + 525 (1250 \sqrt[7]{64 x^{2}}) + 525 (3125 \sqrt[7]{8 x}) + 525 \cdot 3125 - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.10

Simplifique.

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Etapa 5.2.4.10.1

Multiplique $4$ por $525$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 525 (50 \sqrt[7]{32 x^{4}}) + 525 (500 \sqrt[7]{4 x^{3}}) + 525 (1250 \sqrt[7]{64 x^{2}}) + 525 (3125 \sqrt[7]{8 x}) + 525 \cdot 3125 - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.10.2

Multiplique $50$ por $525$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 525 (500 \sqrt[7]{4 x^{3}}) + 525 (1250 \sqrt[7]{64 x^{2}}) + 525 (3125 \sqrt[7]{8 x}) + 525 \cdot 3125 - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.10.3

Multiplique $500$ por $525$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 525 (1250 \sqrt[7]{64 x^{2}}) + 525 (3125 \sqrt[7]{8 x}) + 525 \cdot 3125 - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.10.4

Multiplique $1250$ por $525$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 525 (3125 \sqrt[7]{8 x}) + 525 \cdot 3125 - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.10.5

Multiplique $3125$ por $525$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 525 \cdot 3125 - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.10.6

Multiplique $525$ por $3125$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 4375 {(\sqrt[7]{8 x} + 5)}^{4} + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.11

Use o teorema binomial.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 4375 ({\sqrt[7]{8 x}}^{4} + 4 {\sqrt[7]{8 x}}^{3} \cdot 5 + 6 {\sqrt[7]{8 x}}^{2} \cdot 5^{2} + 4 \sqrt[7]{8 x} \cdot 5^{3} + 5^{4}) + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.12

Simplifique cada termo.

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Etapa 5.2.4.12.1

Reescreva ${\sqrt[7]{8 x}}^{4}$ como $\sqrt[7]{{(8 x)}^{4}}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 4375 (\sqrt[7]{{(8 x)}^{4}} + 4 {\sqrt[7]{8 x}}^{3} \cdot 5 + 6 {\sqrt[7]{8 x}}^{2} \cdot 5^{2} + 4 \sqrt[7]{8 x} \cdot 5^{3} + 5^{4}) + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.12.2

Aplique a regra do produto a $8 x$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 4375 (\sqrt[7]{8^{4} x^{4}} + 4 {\sqrt[7]{8 x}}^{3} \cdot 5 + 6 {\sqrt[7]{8 x}}^{2} \cdot 5^{2} + 4 \sqrt[7]{8 x} \cdot 5^{3} + 5^{4}) + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.12.3

Eleve $8$ à potência de $4$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 4375 (\sqrt[7]{4096 x^{4}} + 4 {\sqrt[7]{8 x}}^{3} \cdot 5 + 6 {\sqrt[7]{8 x}}^{2} \cdot 5^{2} + 4 \sqrt[7]{8 x} \cdot 5^{3} + 5^{4}) + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.12.4

Reescreva $4096 x^{4}$ como $2^{7} \cdot (32 x^{4})$ .

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Etapa 5.2.4.12.4.1

Fatore $128$ de $4096$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 4375 (\sqrt[7]{128 (32) x^{4}} + 4 {\sqrt[7]{8 x}}^{3} \cdot 5 + 6 {\sqrt[7]{8 x}}^{2} \cdot 5^{2} + 4 \sqrt[7]{8 x} \cdot 5^{3} + 5^{4}) + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.12.4.2

Reescreva $128$ como $2^{7}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 4375 (\sqrt[7]{2^{7} \cdot (32 x^{4})} + 4 {\sqrt[7]{8 x}}^{3} \cdot 5 + 6 {\sqrt[7]{8 x}}^{2} \cdot 5^{2} + 4 \sqrt[7]{8 x} \cdot 5^{3} + 5^{4}) + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.12.4.3

Adicione parênteses.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 4375 (\sqrt[7]{2^{7} \cdot (32 x^{4})} + 4 {\sqrt[7]{8 x}}^{3} \cdot 5 + 6 {\sqrt[7]{8 x}}^{2} \cdot 5^{2} + 4 \sqrt[7]{8 x} \cdot 5^{3} + 5^{4}) + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.12.5

Elimine os termos abaixo do radical.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 4375 (2 \sqrt[7]{32 x^{4}} + 4 {\sqrt[7]{8 x}}^{3} \cdot 5 + 6 {\sqrt[7]{8 x}}^{2} \cdot 5^{2} + 4 \sqrt[7]{8 x} \cdot 5^{3} + 5^{4}) + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.12.6

Reescreva ${\sqrt[7]{8 x}}^{3}$ como $\sqrt[7]{{(8 x)}^{3}}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 4375 (2 \sqrt[7]{32 x^{4}} + 4 \sqrt[7]{{(8 x)}^{3}} \cdot 5 + 6 {\sqrt[7]{8 x}}^{2} \cdot 5^{2} + 4 \sqrt[7]{8 x} \cdot 5^{3} + 5^{4}) + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.12.7

Aplique a regra do produto a $8 x$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 4375 (2 \sqrt[7]{32 x^{4}} + 4 \sqrt[7]{8^{3} x^{3}} \cdot 5 + 6 {\sqrt[7]{8 x}}^{2} \cdot 5^{2} + 4 \sqrt[7]{8 x} \cdot 5^{3} + 5^{4}) + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.12.8

Eleve $8$ à potência de $3$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 4375 (2 \sqrt[7]{32 x^{4}} + 4 \sqrt[7]{512 x^{3}} \cdot 5 + 6 {\sqrt[7]{8 x}}^{2} \cdot 5^{2} + 4 \sqrt[7]{8 x} \cdot 5^{3} + 5^{4}) + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.12.9

Reescreva $512 x^{3}$ como $2^{7} \cdot (4 x^{3})$ .

Toque para ver mais passagens...

Etapa 5.2.4.12.9.1

Fatore $128$ de $512$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 4375 (2 \sqrt[7]{32 x^{4}} + 4 \sqrt[7]{128 (4) x^{3}} \cdot 5 + 6 {\sqrt[7]{8 x}}^{2} \cdot 5^{2} + 4 \sqrt[7]{8 x} \cdot 5^{3} + 5^{4}) + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.12.9.2

Reescreva $128$ como $2^{7}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 4375 (2 \sqrt[7]{32 x^{4}} + 4 \sqrt[7]{2^{7} \cdot (4 x^{3})} \cdot 5 + 6 {\sqrt[7]{8 x}}^{2} \cdot 5^{2} + 4 \sqrt[7]{8 x} \cdot 5^{3} + 5^{4}) + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.12.9.3

Adicione parênteses.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 4375 (2 \sqrt[7]{32 x^{4}} + 4 \sqrt[7]{2^{7} \cdot (4 x^{3})} \cdot 5 + 6 {\sqrt[7]{8 x}}^{2} \cdot 5^{2} + 4 \sqrt[7]{8 x} \cdot 5^{3} + 5^{4}) + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.12.10

Elimine os termos abaixo do radical.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 4375 (2 \sqrt[7]{32 x^{4}} + 4 (2 \sqrt[7]{4 x^{3}}) \cdot 5 + 6 {\sqrt[7]{8 x}}^{2} \cdot 5^{2} + 4 \sqrt[7]{8 x} \cdot 5^{3} + 5^{4}) + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.12.11

Multiplique $2$ por $4$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 4375 (2 \sqrt[7]{32 x^{4}} + 8 \sqrt[7]{4 x^{3}} \cdot 5 + 6 {\sqrt[7]{8 x}}^{2} \cdot 5^{2} + 4 \sqrt[7]{8 x} \cdot 5^{3} + 5^{4}) + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.12.12

Multiplique $5$ por $8$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 4375 (2 \sqrt[7]{32 x^{4}} + 40 \sqrt[7]{4 x^{3}} + 6 {\sqrt[7]{8 x}}^{2} \cdot 5^{2} + 4 \sqrt[7]{8 x} \cdot 5^{3} + 5^{4}) + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.12.13

Reescreva ${\sqrt[7]{8 x}}^{2}$ como $\sqrt[7]{{(8 x)}^{2}}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 4375 (2 \sqrt[7]{32 x^{4}} + 40 \sqrt[7]{4 x^{3}} + 6 \sqrt[7]{{(8 x)}^{2}} \cdot 5^{2} + 4 \sqrt[7]{8 x} \cdot 5^{3} + 5^{4}) + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.12.14

Aplique a regra do produto a $8 x$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 4375 (2 \sqrt[7]{32 x^{4}} + 40 \sqrt[7]{4 x^{3}} + 6 \sqrt[7]{8^{2} x^{2}} \cdot 5^{2} + 4 \sqrt[7]{8 x} \cdot 5^{3} + 5^{4}) + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.12.15

Eleve $8$ à potência de $2$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 4375 (2 \sqrt[7]{32 x^{4}} + 40 \sqrt[7]{4 x^{3}} + 6 \sqrt[7]{64 x^{2}} \cdot 5^{2} + 4 \sqrt[7]{8 x} \cdot 5^{3} + 5^{4}) + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.12.16

Eleve $5$ à potência de $2$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 4375 (2 \sqrt[7]{32 x^{4}} + 40 \sqrt[7]{4 x^{3}} + 6 \sqrt[7]{64 x^{2}} \cdot 25 + 4 \sqrt[7]{8 x} \cdot 5^{3} + 5^{4}) + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.12.17

Multiplique $25$ por $6$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 4375 (2 \sqrt[7]{32 x^{4}} + 40 \sqrt[7]{4 x^{3}} + 150 \sqrt[7]{64 x^{2}} + 4 \sqrt[7]{8 x} \cdot 5^{3} + 5^{4}) + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.12.18

Eleve $5$ à potência de $3$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 4375 (2 \sqrt[7]{32 x^{4}} + 40 \sqrt[7]{4 x^{3}} + 150 \sqrt[7]{64 x^{2}} + 4 \sqrt[7]{8 x} \cdot 125 + 5^{4}) + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.12.19

Multiplique $125$ por $4$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 4375 (2 \sqrt[7]{32 x^{4}} + 40 \sqrt[7]{4 x^{3}} + 150 \sqrt[7]{64 x^{2}} + 500 \sqrt[7]{8 x} + 5^{4}) + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.12.20

Eleve $5$ à potência de $4$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 4375 (2 \sqrt[7]{32 x^{4}} + 40 \sqrt[7]{4 x^{3}} + 150 \sqrt[7]{64 x^{2}} + 500 \sqrt[7]{8 x} + 625) + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.13

Aplique a propriedade distributiva.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 4375 (2 \sqrt[7]{32 x^{4}}) - 4375 (40 \sqrt[7]{4 x^{3}}) - 4375 (150 \sqrt[7]{64 x^{2}}) - 4375 (500 \sqrt[7]{8 x}) - 4375 \cdot 625 + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.14

Simplifique.

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Etapa 5.2.4.14.1

Multiplique $2$ por $- 4375$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 4375 (40 \sqrt[7]{4 x^{3}}) - 4375 (150 \sqrt[7]{64 x^{2}}) - 4375 (500 \sqrt[7]{8 x}) - 4375 \cdot 625 + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.14.2

Multiplique $40$ por $- 4375$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 4375 (150 \sqrt[7]{64 x^{2}}) - 4375 (500 \sqrt[7]{8 x}) - 4375 \cdot 625 + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.14.3

Multiplique $150$ por $- 4375$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 4375 (500 \sqrt[7]{8 x}) - 4375 \cdot 625 + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.14.4

Multiplique $500$ por $- 4375$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 4375 \cdot 625 + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.14.5

Multiplique $- 4375$ por $625$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 21875 {(\sqrt[7]{8 x} + 5)}^{3} - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.15

Use o teorema binomial.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 21875 ({\sqrt[7]{8 x}}^{3} + 3 {\sqrt[7]{8 x}}^{2} \cdot 5 + 3 \sqrt[7]{8 x} \cdot 5^{2} + 5^{3}) - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.16

Simplifique cada termo.

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Etapa 5.2.4.16.1

Reescreva ${\sqrt[7]{8 x}}^{3}$ como $\sqrt[7]{{(8 x)}^{3}}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 21875 (\sqrt[7]{{(8 x)}^{3}} + 3 {\sqrt[7]{8 x}}^{2} \cdot 5 + 3 \sqrt[7]{8 x} \cdot 5^{2} + 5^{3}) - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.16.2

Aplique a regra do produto a $8 x$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 21875 (\sqrt[7]{8^{3} x^{3}} + 3 {\sqrt[7]{8 x}}^{2} \cdot 5 + 3 \sqrt[7]{8 x} \cdot 5^{2} + 5^{3}) - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.16.3

Eleve $8$ à potência de $3$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 21875 (\sqrt[7]{512 x^{3}} + 3 {\sqrt[7]{8 x}}^{2} \cdot 5 + 3 \sqrt[7]{8 x} \cdot 5^{2} + 5^{3}) - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.16.4

Reescreva $512 x^{3}$ como $2^{7} \cdot (4 x^{3})$ .

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Etapa 5.2.4.16.4.1

Fatore $128$ de $512$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 21875 (\sqrt[7]{128 (4) x^{3}} + 3 {\sqrt[7]{8 x}}^{2} \cdot 5 + 3 \sqrt[7]{8 x} \cdot 5^{2} + 5^{3}) - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.16.4.2

Reescreva $128$ como $2^{7}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 21875 (\sqrt[7]{2^{7} \cdot (4 x^{3})} + 3 {\sqrt[7]{8 x}}^{2} \cdot 5 + 3 \sqrt[7]{8 x} \cdot 5^{2} + 5^{3}) - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.16.4.3

Adicione parênteses.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 21875 (\sqrt[7]{2^{7} \cdot (4 x^{3})} + 3 {\sqrt[7]{8 x}}^{2} \cdot 5 + 3 \sqrt[7]{8 x} \cdot 5^{2} + 5^{3}) - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.16.5

Elimine os termos abaixo do radical.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 21875 (2 \sqrt[7]{4 x^{3}} + 3 {\sqrt[7]{8 x}}^{2} \cdot 5 + 3 \sqrt[7]{8 x} \cdot 5^{2} + 5^{3}) - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.16.6

Reescreva ${\sqrt[7]{8 x}}^{2}$ como $\sqrt[7]{{(8 x)}^{2}}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 21875 (2 \sqrt[7]{4 x^{3}} + 3 \sqrt[7]{{(8 x)}^{2}} \cdot 5 + 3 \sqrt[7]{8 x} \cdot 5^{2} + 5^{3}) - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.16.7

Aplique a regra do produto a $8 x$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 21875 (2 \sqrt[7]{4 x^{3}} + 3 \sqrt[7]{8^{2} x^{2}} \cdot 5 + 3 \sqrt[7]{8 x} \cdot 5^{2} + 5^{3}) - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.16.8

Eleve $8$ à potência de $2$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 21875 (2 \sqrt[7]{4 x^{3}} + 3 \sqrt[7]{64 x^{2}} \cdot 5 + 3 \sqrt[7]{8 x} \cdot 5^{2} + 5^{3}) - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.16.9

Multiplique $5$ por $3$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 21875 (2 \sqrt[7]{4 x^{3}} + 15 \sqrt[7]{64 x^{2}} + 3 \sqrt[7]{8 x} \cdot 5^{2} + 5^{3}) - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.16.10

Eleve $5$ à potência de $2$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 21875 (2 \sqrt[7]{4 x^{3}} + 15 \sqrt[7]{64 x^{2}} + 3 \sqrt[7]{8 x} \cdot 25 + 5^{3}) - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.16.11

Multiplique $25$ por $3$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 21875 (2 \sqrt[7]{4 x^{3}} + 15 \sqrt[7]{64 x^{2}} + 75 \sqrt[7]{8 x} + 5^{3}) - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.16.12

Eleve $5$ à potência de $3$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 21875 (2 \sqrt[7]{4 x^{3}} + 15 \sqrt[7]{64 x^{2}} + 75 \sqrt[7]{8 x} + 125) - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.17

Aplique a propriedade distributiva.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 21875 (2 \sqrt[7]{4 x^{3}}) + 21875 (15 \sqrt[7]{64 x^{2}}) + 21875 (75 \sqrt[7]{8 x}) + 21875 \cdot 125 - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.18

Simplifique.

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Etapa 5.2.4.18.1

Multiplique $2$ por $21875$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 43750 \sqrt[7]{4 x^{3}} + 21875 (15 \sqrt[7]{64 x^{2}}) + 21875 (75 \sqrt[7]{8 x}) + 21875 \cdot 125 - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.18.2

Multiplique $15$ por $21875$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 43750 \sqrt[7]{4 x^{3}} + 328125 \sqrt[7]{64 x^{2}} + 21875 (75 \sqrt[7]{8 x}) + 21875 \cdot 125 - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.18.3

Multiplique $75$ por $21875$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 43750 \sqrt[7]{4 x^{3}} + 328125 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 21875 \cdot 125 - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.18.4

Multiplique $21875$ por $125$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 43750 \sqrt[7]{4 x^{3}} + 328125 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 2734375 - 65625 {(\sqrt[7]{8 x} + 5)}^{2} + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.19

Reescreva ${(\sqrt[7]{8 x} + 5)}^{2}$ como $(\sqrt[7]{8 x} + 5) (\sqrt[7]{8 x} + 5)$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 43750 \sqrt[7]{4 x^{3}} + 328125 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 2734375 - 65625 ((\sqrt[7]{8 x} + 5) (\sqrt[7]{8 x} + 5)) + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.20

Expanda $(\sqrt[7]{8 x} + 5) (\sqrt[7]{8 x} + 5)$ usando o método FOIL.

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Etapa 5.2.4.20.1

Aplique a propriedade distributiva.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 43750 \sqrt[7]{4 x^{3}} + 328125 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 2734375 - 65625 (\sqrt[7]{8 x} (\sqrt[7]{8 x} + 5) + 5 (\sqrt[7]{8 x} + 5)) + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.20.2

Aplique a propriedade distributiva.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 43750 \sqrt[7]{4 x^{3}} + 328125 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 2734375 - 65625 (\sqrt[7]{8 x} \sqrt[7]{8 x} + \sqrt[7]{8 x} \cdot 5 + 5 (\sqrt[7]{8 x} + 5)) + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.20.3

Aplique a propriedade distributiva.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 43750 \sqrt[7]{4 x^{3}} + 328125 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 2734375 - 65625 (\sqrt[7]{8 x} \sqrt[7]{8 x} + \sqrt[7]{8 x} \cdot 5 + 5 \sqrt[7]{8 x} + 5 \cdot 5) + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.21

Simplifique e combine termos semelhantes.

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Etapa 5.2.4.21.1

Simplifique cada termo.

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Etapa 5.2.4.21.1.1

Multiplique $\sqrt[7]{8 x} \sqrt[7]{8 x}$ .

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Etapa 5.2.4.21.1.1.1

Eleve $\sqrt[7]{8 x}$ à potência de $1$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 43750 \sqrt[7]{4 x^{3}} + 328125 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 2734375 - 65625 (\sqrt[7]{8 x} \sqrt[7]{8 x} + \sqrt[7]{8 x} \cdot 5 + 5 \sqrt[7]{8 x} + 5 \cdot 5) + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.21.1.1.2

Eleve $\sqrt[7]{8 x}$ à potência de $1$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 43750 \sqrt[7]{4 x^{3}} + 328125 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 2734375 - 65625 (\sqrt[7]{8 x} \sqrt[7]{8 x} + \sqrt[7]{8 x} \cdot 5 + 5 \sqrt[7]{8 x} + 5 \cdot 5) + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.21.1.1.3

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 43750 \sqrt[7]{4 x^{3}} + 328125 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 2734375 - 65625 ({\sqrt[7]{8 x}}^{1 + 1} + \sqrt[7]{8 x} \cdot 5 + 5 \sqrt[7]{8 x} + 5 \cdot 5) + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.21.1.1.4

Some $1$ e $1$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 43750 \sqrt[7]{4 x^{3}} + 328125 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 2734375 - 65625 ({\sqrt[7]{8 x}}^{2} + \sqrt[7]{8 x} \cdot 5 + 5 \sqrt[7]{8 x} + 5 \cdot 5) + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.21.1.2

Reescreva ${\sqrt[7]{8 x}}^{2}$ como $\sqrt[7]{{(8 x)}^{2}}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 43750 \sqrt[7]{4 x^{3}} + 328125 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 2734375 - 65625 (\sqrt[7]{{(8 x)}^{2}} + \sqrt[7]{8 x} \cdot 5 + 5 \sqrt[7]{8 x} + 5 \cdot 5) + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.21.1.3

Aplique a regra do produto a $8 x$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 43750 \sqrt[7]{4 x^{3}} + 328125 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 2734375 - 65625 (\sqrt[7]{8^{2} x^{2}} + \sqrt[7]{8 x} \cdot 5 + 5 \sqrt[7]{8 x} + 5 \cdot 5) + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.21.1.4

Eleve $8$ à potência de $2$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 43750 \sqrt[7]{4 x^{3}} + 328125 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 2734375 - 65625 (\sqrt[7]{64 x^{2}} + \sqrt[7]{8 x} \cdot 5 + 5 \sqrt[7]{8 x} + 5 \cdot 5) + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.21.1.5

Mova $5$ para a esquerda de $\sqrt[7]{8 x}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 43750 \sqrt[7]{4 x^{3}} + 328125 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 2734375 - 65625 (\sqrt[7]{64 x^{2}} + 5 \cdot \sqrt[7]{8 x} + 5 \sqrt[7]{8 x} + 5 \cdot 5) + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.21.1.6

Multiplique $5$ por $5$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 43750 \sqrt[7]{4 x^{3}} + 328125 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 2734375 - 65625 (\sqrt[7]{64 x^{2}} + 5 \sqrt[7]{8 x} + 5 \sqrt[7]{8 x} + 25) + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.21.2

Some $5 \sqrt[7]{8 x}$ e $5 \sqrt[7]{8 x}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 43750 \sqrt[7]{4 x^{3}} + 328125 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 2734375 - 65625 (\sqrt[7]{64 x^{2}} + 10 \sqrt[7]{8 x} + 25) + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.22

Aplique a propriedade distributiva.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 43750 \sqrt[7]{4 x^{3}} + 328125 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 2734375 - 65625 \sqrt[7]{64 x^{2}} - 65625 (10 \sqrt[7]{8 x}) - 65625 \cdot 25 + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.23

Simplifique.

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Etapa 5.2.4.23.1

Multiplique $10$ por $- 65625$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 43750 \sqrt[7]{4 x^{3}} + 328125 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 2734375 - 65625 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 65625 \cdot 25 + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.23.2

Multiplique $- 65625$ por $25$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 43750 \sqrt[7]{4 x^{3}} + 328125 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 2734375 - 65625 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 1640625 + 109375 (\sqrt[7]{8 x} + 5) - 78125}{8}$

Etapa 5.2.4.24

Aplique a propriedade distributiva.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 43750 \sqrt[7]{4 x^{3}} + 328125 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 2734375 - 65625 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 1640625 + 109375 \sqrt[7]{8 x} + 109375 \cdot 5 - 78125}{8}$

Etapa 5.2.4.25

Multiplique $109375$ por $5$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 43750 \sqrt[7]{4 x^{3}} + 328125 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 2734375 - 65625 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 1640625 + 109375 \sqrt[7]{8 x} + 546875 - 78125}{8}$

Etapa 5.2.5

Simplifique os termos.

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Etapa 5.2.5.1

Combine os termos opostos em $8 x + 140 \sqrt[7]{16 x^{6}} + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 140 \sqrt[7]{16 x^{6}} - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 43750 \sqrt[7]{4 x^{3}} + 328125 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 2734375 - 65625 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 1640625 + 109375 \sqrt[7]{8 x} + 546875 - 78125$ .

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Etapa 5.2.5.1.1

Subtraia $140 \sqrt[7]{16 x^{6}}$ de $140 \sqrt[7]{16 x^{6}}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 0 + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 43750 \sqrt[7]{4 x^{3}} + 328125 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 2734375 - 65625 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 1640625 + 109375 \sqrt[7]{8 x} + 546875 - 78125}{8}$

Etapa 5.2.5.1.2

Some $8 x$ e $0$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 4200 \sqrt[7]{2 x^{5}} - 26250 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 26250 \sqrt[7]{32 x^{4}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 43750 \sqrt[7]{4 x^{3}} + 328125 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 2734375 - 65625 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 1640625 + 109375 \sqrt[7]{8 x} + 546875 - 78125}{8}$

Etapa 5.2.5.1.3

Some $- 26250 \sqrt[7]{32 x^{4}}$ e $26250 \sqrt[7]{32 x^{4}}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 4200 \sqrt[7]{2 x^{5}} + 0 - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 43750 \sqrt[7]{4 x^{3}} + 328125 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 2734375 - 65625 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 1640625 + 109375 \sqrt[7]{8 x} + 546875 - 78125}{8}$

Etapa 5.2.5.1.4

Some $8 x + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 4200 \sqrt[7]{2 x^{5}}$ e $0$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 2100 \sqrt[7]{2 x^{5}} + 8750 \sqrt[7]{32 x^{4}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 4200 \sqrt[7]{2 x^{5}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 8750 \sqrt[7]{32 x^{4}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 43750 \sqrt[7]{4 x^{3}} + 328125 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 2734375 - 65625 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 1640625 + 109375 \sqrt[7]{8 x} + 546875 - 78125}{8}$

Etapa 5.2.5.1.5

Subtraia $8750 \sqrt[7]{32 x^{4}}$ de $8750 \sqrt[7]{32 x^{4}}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 2100 \sqrt[7]{2 x^{5}} + 0 + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 4200 \sqrt[7]{2 x^{5}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 43750 \sqrt[7]{4 x^{3}} + 328125 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 2734375 - 65625 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 1640625 + 109375 \sqrt[7]{8 x} + 546875 - 78125}{8}$

Etapa 5.2.5.1.6

Some $8 x + 2100 \sqrt[7]{2 x^{5}}$ e $0$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 2100 \sqrt[7]{2 x^{5}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 4200 \sqrt[7]{2 x^{5}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 262500 \sqrt[7]{4 x^{3}} + 656250 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 1640625 - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{64 x^{2}} - 2187500 \sqrt[7]{8 x} - 2734375 + 43750 \sqrt[7]{4 x^{3}} + 328125 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 2734375 - 65625 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 1640625 + 109375 \sqrt[7]{8 x} + 546875 - 78125}{8}$

Etapa 5.2.5.1.7

Subtraia $656250 \sqrt[7]{64 x^{2}}$ de $656250 \sqrt[7]{64 x^{2}}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 2100 \sqrt[7]{2 x^{5}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 4200 \sqrt[7]{2 x^{5}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 262500 \sqrt[7]{4 x^{3}} + 0 + 1640625 \sqrt[7]{8 x} + 1640625 - 175000 \sqrt[7]{4 x^{3}} - 2187500 \sqrt[7]{8 x} - 2734375 + 43750 \sqrt[7]{4 x^{3}} + 328125 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 2734375 - 65625 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 1640625 + 109375 \sqrt[7]{8 x} + 546875 - 78125}{8}$

Etapa 5.2.5.1.8

Some $8 x + 2100 \sqrt[7]{2 x^{5}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 4200 \sqrt[7]{2 x^{5}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 262500 \sqrt[7]{4 x^{3}}$ e $0$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 2100 \sqrt[7]{2 x^{5}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 4200 \sqrt[7]{2 x^{5}} - 175000 \sqrt[7]{4 x^{3}} - 328125 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 262500 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} + 1640625 - 175000 \sqrt[7]{4 x^{3}} - 2187500 \sqrt[7]{8 x} - 2734375 + 43750 \sqrt[7]{4 x^{3}} + 328125 \sqrt[7]{64 x^{2}} + 1640625 \sqrt[7]{8 x} + 2734375 - 65625 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 1640625 + 109375 \sqrt[7]{8 x} + 546875 - 78125}{8}$

Etapa 5.2.5.1.9

Some $- 328125 \sqrt[7]{64 x^{2}}$ e $328125 \sqrt[7]{64 x^{2}}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 2100 \sqrt[7]{2 x^{5}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 4200 \sqrt[7]{2 x^{5}} - 175000 \sqrt[7]{4 x^{3}} + 0 - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 262500 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} + 1640625 - 175000 \sqrt[7]{4 x^{3}} - 2187500 \sqrt[7]{8 x} - 2734375 + 43750 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} + 2734375 - 65625 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 1640625 + 109375 \sqrt[7]{8 x} + 546875 - 78125}{8}$

Etapa 5.2.5.1.10

Some $8 x + 2100 \sqrt[7]{2 x^{5}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 4200 \sqrt[7]{2 x^{5}} - 175000 \sqrt[7]{4 x^{3}}$ e $0$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 2100 \sqrt[7]{2 x^{5}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 4200 \sqrt[7]{2 x^{5}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 262500 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} + 1640625 - 175000 \sqrt[7]{4 x^{3}} - 2187500 \sqrt[7]{8 x} - 2734375 + 43750 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} + 2734375 - 65625 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 1640625 + 109375 \sqrt[7]{8 x} + 546875 - 78125}{8}$

Etapa 5.2.5.1.11

Some $- 2734375$ e $2734375$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 2100 \sqrt[7]{2 x^{5}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 4200 \sqrt[7]{2 x^{5}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 262500 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} + 1640625 - 175000 \sqrt[7]{4 x^{3}} - 2187500 \sqrt[7]{8 x} + 0 + 43750 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} - 65625 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 1640625 + 109375 \sqrt[7]{8 x} + 546875 - 78125}{8}$

Etapa 5.2.5.1.12

Some $8 x + 2100 \sqrt[7]{2 x^{5}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 4200 \sqrt[7]{2 x^{5}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 262500 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} + 1640625 - 175000 \sqrt[7]{4 x^{3}} - 2187500 \sqrt[7]{8 x}$ e $0$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 2100 \sqrt[7]{2 x^{5}} + 43750 \sqrt[7]{4 x^{3}} + 65625 \sqrt[7]{64 x^{2}} + 109375 \sqrt[7]{8 x} + 78125 - 4200 \sqrt[7]{2 x^{5}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 262500 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} + 1640625 - 175000 \sqrt[7]{4 x^{3}} - 2187500 \sqrt[7]{8 x} + 43750 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} - 65625 \sqrt[7]{64 x^{2}} - 656250 \sqrt[7]{8 x} - 1640625 + 109375 \sqrt[7]{8 x} + 546875 - 78125}{8}$

Etapa 5.2.5.1.13

Subtraia $65625 \sqrt[7]{64 x^{2}}$ de $65625 \sqrt[7]{64 x^{2}}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 2100 \sqrt[7]{2 x^{5}} + 43750 \sqrt[7]{4 x^{3}} + 0 + 109375 \sqrt[7]{8 x} + 78125 - 4200 \sqrt[7]{2 x^{5}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 262500 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} + 1640625 - 175000 \sqrt[7]{4 x^{3}} - 2187500 \sqrt[7]{8 x} + 43750 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} - 656250 \sqrt[7]{8 x} - 1640625 + 109375 \sqrt[7]{8 x} + 546875 - 78125}{8}$

Etapa 5.2.5.1.14

Some $8 x + 2100 \sqrt[7]{2 x^{5}} + 43750 \sqrt[7]{4 x^{3}}$ e $0$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 2100 \sqrt[7]{2 x^{5}} + 43750 \sqrt[7]{4 x^{3}} + 109375 \sqrt[7]{8 x} + 78125 - 4200 \sqrt[7]{2 x^{5}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 262500 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} + 1640625 - 175000 \sqrt[7]{4 x^{3}} - 2187500 \sqrt[7]{8 x} + 43750 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} - 656250 \sqrt[7]{8 x} - 1640625 + 109375 \sqrt[7]{8 x} + 546875 - 78125}{8}$

Etapa 5.2.5.1.15

Subtraia $1640625$ de $1640625$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 2100 \sqrt[7]{2 x^{5}} + 43750 \sqrt[7]{4 x^{3}} + 109375 \sqrt[7]{8 x} + 78125 - 4200 \sqrt[7]{2 x^{5}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 262500 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} + 0 - 175000 \sqrt[7]{4 x^{3}} - 2187500 \sqrt[7]{8 x} + 43750 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} - 656250 \sqrt[7]{8 x} + 109375 \sqrt[7]{8 x} + 546875 - 78125}{8}$

Etapa 5.2.5.1.16

Some $8 x + 2100 \sqrt[7]{2 x^{5}} + 43750 \sqrt[7]{4 x^{3}} + 109375 \sqrt[7]{8 x} + 78125 - 4200 \sqrt[7]{2 x^{5}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 262500 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x}$ e $0$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 2100 \sqrt[7]{2 x^{5}} + 43750 \sqrt[7]{4 x^{3}} + 109375 \sqrt[7]{8 x} + 78125 - 4200 \sqrt[7]{2 x^{5}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{8 x} - 546875 + 2100 \sqrt[7]{2 x^{5}} + 262500 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} - 175000 \sqrt[7]{4 x^{3}} - 2187500 \sqrt[7]{8 x} + 43750 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} - 656250 \sqrt[7]{8 x} + 109375 \sqrt[7]{8 x} + 546875 - 78125}{8}$

Etapa 5.2.5.1.17

Some $- 546875$ e $546875$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 2100 \sqrt[7]{2 x^{5}} + 43750 \sqrt[7]{4 x^{3}} + 109375 \sqrt[7]{8 x} + 78125 - 4200 \sqrt[7]{2 x^{5}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{8 x} + 0 + 2100 \sqrt[7]{2 x^{5}} + 262500 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} - 175000 \sqrt[7]{4 x^{3}} - 2187500 \sqrt[7]{8 x} + 43750 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} - 656250 \sqrt[7]{8 x} + 109375 \sqrt[7]{8 x} - 78125}{8}$

Etapa 5.2.5.1.18

Some $8 x + 2100 \sqrt[7]{2 x^{5}} + 43750 \sqrt[7]{4 x^{3}} + 109375 \sqrt[7]{8 x} + 78125 - 4200 \sqrt[7]{2 x^{5}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{8 x}$ e $0$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 2100 \sqrt[7]{2 x^{5}} + 43750 \sqrt[7]{4 x^{3}} + 109375 \sqrt[7]{8 x} + 78125 - 4200 \sqrt[7]{2 x^{5}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{8 x} + 2100 \sqrt[7]{2 x^{5}} + 262500 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} - 175000 \sqrt[7]{4 x^{3}} - 2187500 \sqrt[7]{8 x} + 43750 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} - 656250 \sqrt[7]{8 x} + 109375 \sqrt[7]{8 x} - 78125}{8}$

Etapa 5.2.5.1.19

Subtraia $78125$ de $78125$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 2100 \sqrt[7]{2 x^{5}} + 43750 \sqrt[7]{4 x^{3}} + 109375 \sqrt[7]{8 x} + 0 - 4200 \sqrt[7]{2 x^{5}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{8 x} + 2100 \sqrt[7]{2 x^{5}} + 262500 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} - 175000 \sqrt[7]{4 x^{3}} - 2187500 \sqrt[7]{8 x} + 43750 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} - 656250 \sqrt[7]{8 x} + 109375 \sqrt[7]{8 x}}{8}$

Etapa 5.2.5.1.20

Some $8 x + 2100 \sqrt[7]{2 x^{5}} + 43750 \sqrt[7]{4 x^{3}} + 109375 \sqrt[7]{8 x}$ e $0$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 2100 \sqrt[7]{2 x^{5}} + 43750 \sqrt[7]{4 x^{3}} + 109375 \sqrt[7]{8 x} - 4200 \sqrt[7]{2 x^{5}} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{8 x} + 2100 \sqrt[7]{2 x^{5}} + 262500 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} - 175000 \sqrt[7]{4 x^{3}} - 2187500 \sqrt[7]{8 x} + 43750 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} - 656250 \sqrt[7]{8 x} + 109375 \sqrt[7]{8 x}}{8}$

Etapa 5.2.5.2

Subtraia $4200 \sqrt[7]{2 x^{5}}$ de $2100 \sqrt[7]{2 x^{5}}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x - 2100 \sqrt[7]{2 x^{5}} + 43750 \sqrt[7]{4 x^{3}} + 109375 \sqrt[7]{8 x} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{8 x} + 2100 \sqrt[7]{2 x^{5}} + 262500 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} - 175000 \sqrt[7]{4 x^{3}} - 2187500 \sqrt[7]{8 x} + 43750 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} - 656250 \sqrt[7]{8 x} + 109375 \sqrt[7]{8 x}}{8}$

Etapa 5.2.5.3

Combine os termos opostos em $8 x - 2100 \sqrt[7]{2 x^{5}} + 43750 \sqrt[7]{4 x^{3}} + 109375 \sqrt[7]{8 x} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{8 x} + 2100 \sqrt[7]{2 x^{5}} + 262500 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} - 175000 \sqrt[7]{4 x^{3}} - 2187500 \sqrt[7]{8 x} + 43750 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} - 656250 \sqrt[7]{8 x} + 109375 \sqrt[7]{8 x}$ .

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Etapa 5.2.5.3.1

Some $- 2100 \sqrt[7]{2 x^{5}}$ e $2100 \sqrt[7]{2 x^{5}}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 0 + 43750 \sqrt[7]{4 x^{3}} + 109375 \sqrt[7]{8 x} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{8 x} + 262500 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} - 175000 \sqrt[7]{4 x^{3}} - 2187500 \sqrt[7]{8 x} + 43750 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} - 656250 \sqrt[7]{8 x} + 109375 \sqrt[7]{8 x}}{8}$

Etapa 5.2.5.3.2

Some $8 x$ e $0$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 43750 \sqrt[7]{4 x^{3}} + 109375 \sqrt[7]{8 x} - 175000 \sqrt[7]{4 x^{3}} - 656250 \sqrt[7]{8 x} + 262500 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} - 175000 \sqrt[7]{4 x^{3}} - 2187500 \sqrt[7]{8 x} + 43750 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} - 656250 \sqrt[7]{8 x} + 109375 \sqrt[7]{8 x}}{8}$

Etapa 5.2.5.4

Subtraia $175000 \sqrt[7]{4 x^{3}}$ de $43750 \sqrt[7]{4 x^{3}}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x - 131250 \sqrt[7]{4 x^{3}} + 109375 \sqrt[7]{8 x} - 656250 \sqrt[7]{8 x} + 262500 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} - 175000 \sqrt[7]{4 x^{3}} - 2187500 \sqrt[7]{8 x} + 43750 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} - 656250 \sqrt[7]{8 x} + 109375 \sqrt[7]{8 x}}{8}$

Etapa 5.2.5.5

Some $- 131250 \sqrt[7]{4 x^{3}}$ e $262500 \sqrt[7]{4 x^{3}}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 131250 \sqrt[7]{4 x^{3}} + 109375 \sqrt[7]{8 x} - 656250 \sqrt[7]{8 x} + 1640625 \sqrt[7]{8 x} - 175000 \sqrt[7]{4 x^{3}} - 2187500 \sqrt[7]{8 x} + 43750 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} - 656250 \sqrt[7]{8 x} + 109375 \sqrt[7]{8 x}}{8}$

Etapa 5.2.5.6

Subtraia $175000 \sqrt[7]{4 x^{3}}$ de $131250 \sqrt[7]{4 x^{3}}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x - 43750 \sqrt[7]{4 x^{3}} + 109375 \sqrt[7]{8 x} - 656250 \sqrt[7]{8 x} + 1640625 \sqrt[7]{8 x} - 2187500 \sqrt[7]{8 x} + 43750 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} - 656250 \sqrt[7]{8 x} + 109375 \sqrt[7]{8 x}}{8}$

Etapa 5.2.5.7

Combine os termos opostos em $8 x - 43750 \sqrt[7]{4 x^{3}} + 109375 \sqrt[7]{8 x} - 656250 \sqrt[7]{8 x} + 1640625 \sqrt[7]{8 x} - 2187500 \sqrt[7]{8 x} + 43750 \sqrt[7]{4 x^{3}} + 1640625 \sqrt[7]{8 x} - 656250 \sqrt[7]{8 x} + 109375 \sqrt[7]{8 x}$ .

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Etapa 5.2.5.7.1

Some $- 43750 \sqrt[7]{4 x^{3}}$ e $43750 \sqrt[7]{4 x^{3}}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 0 + 109375 \sqrt[7]{8 x} - 656250 \sqrt[7]{8 x} + 1640625 \sqrt[7]{8 x} - 2187500 \sqrt[7]{8 x} + 1640625 \sqrt[7]{8 x} - 656250 \sqrt[7]{8 x} + 109375 \sqrt[7]{8 x}}{8}$

Etapa 5.2.5.7.2

Some $8 x$ e $0$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 109375 \sqrt[7]{8 x} - 656250 \sqrt[7]{8 x} + 1640625 \sqrt[7]{8 x} - 2187500 \sqrt[7]{8 x} + 1640625 \sqrt[7]{8 x} - 656250 \sqrt[7]{8 x} + 109375 \sqrt[7]{8 x}}{8}$

Etapa 5.2.5.8

Subtraia $656250 \sqrt[7]{8 x}$ de $109375 \sqrt[7]{8 x}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x - 546875 \sqrt[7]{8 x} + 1640625 \sqrt[7]{8 x} - 2187500 \sqrt[7]{8 x} + 1640625 \sqrt[7]{8 x} - 656250 \sqrt[7]{8 x} + 109375 \sqrt[7]{8 x}}{8}$

Etapa 5.2.5.9

Some $- 546875 \sqrt[7]{8 x}$ e $1640625 \sqrt[7]{8 x}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 1093750 \sqrt[7]{8 x} - 2187500 \sqrt[7]{8 x} + 1640625 \sqrt[7]{8 x} - 656250 \sqrt[7]{8 x} + 109375 \sqrt[7]{8 x}}{8}$

Etapa 5.2.5.10

Subtraia $2187500 \sqrt[7]{8 x}$ de $1093750 \sqrt[7]{8 x}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x - 1093750 \sqrt[7]{8 x} + 1640625 \sqrt[7]{8 x} - 656250 \sqrt[7]{8 x} + 109375 \sqrt[7]{8 x}}{8}$

Etapa 5.2.5.11

Some $- 1093750 \sqrt[7]{8 x}$ e $1640625 \sqrt[7]{8 x}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 546875 \sqrt[7]{8 x} - 656250 \sqrt[7]{8 x} + 109375 \sqrt[7]{8 x}}{8}$

Etapa 5.2.5.12

Subtraia $656250 \sqrt[7]{8 x}$ de $546875 \sqrt[7]{8 x}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x - 109375 \sqrt[7]{8 x} + 109375 \sqrt[7]{8 x}}{8}$

Etapa 5.2.5.13

Combine os termos opostos em $8 x - 109375 \sqrt[7]{8 x} + 109375 \sqrt[7]{8 x}$ .

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Etapa 5.2.5.13.1

Some $- 109375 \sqrt[7]{8 x}$ e $109375 \sqrt[7]{8 x}$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x + 0}{8}$

Etapa 5.2.5.13.2

Some $8 x$ e $0$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x}{8}$

Etapa 5.2.5.14

Cancele o fator comum de $8$ .

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Etapa 5.2.5.14.1

Cancele o fator comum.

$f^{- 1} (\sqrt[7]{8 x} + 5) = \frac{8 x}{8}$

Etapa 5.2.5.14.2

Divida $x$ por $1$ .

$f^{- 1} (\sqrt[7]{8 x} + 5) = x$

Etapa 5.3

Avalie $f (f^{- 1} (x))$ .

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Etapa 5.3.1

Estabeleça a função do resultado composto.

$f (f^{- 1} (x))$

Etapa 5.3.2

Avalie $f (\frac{x^{7}}{8} - \frac{35 x^{6}}{8} + \frac{525 x^{5}}{8} - \frac{4375 x^{4}}{8} + \frac{21875 x^{3}}{8} - \frac{65625 x^{2}}{8} + \frac{109375 x}{8} - \frac{78125}{8})$ substituindo o valor de $f^{- 1}$ em $f$ .

$f (\frac{x^{7}}{8} - \frac{35 x^{6}}{8} + \frac{525 x^{5}}{8} - \frac{4375 x^{4}}{8} + \frac{21875 x^{3}}{8} - \frac{65625 x^{2}}{8} + \frac{109375 x}{8} - \frac{78125}{8}) = \sqrt[7]{8 (\frac{x^{7}}{8} - \frac{35 x^{6}}{8} + \frac{525 x^{5}}{8} - \frac{4375 x^{4}}{8} + \frac{21875 x^{3}}{8} - \frac{65625 x^{2}}{8} + \frac{109375 x}{8} - \frac{78125}{8})} + 5$

Etapa 5.3.3

Simplifique cada termo.

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Etapa 5.3.3.1

Combine os numeradores em relação ao denominador comum.

$f (\frac{x^{7}}{8} - \frac{35 x^{6}}{8} + \frac{525 x^{5}}{8} - \frac{4375 x^{4}}{8} + \frac{21875 x^{3}}{8} - \frac{65625 x^{2}}{8} + \frac{109375 x}{8} - \frac{78125}{8}) = \sqrt[7]{8 (\frac{x^{7} - 35 x^{6} + 525 x^{5} - 4375 x^{4} + 21875 x^{3} - 65625 x^{2} + 109375 x - 78125}{8})} + 5$

Etapa 5.3.3.2

Simplifique o numerador.

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Etapa 5.3.3.2.1

Associe cada termo aos termos da fórmula do teorema binomial.

$f (\frac{x^{7}}{8} - \frac{35 x^{6}}{8} + \frac{525 x^{5}}{8} - \frac{4375 x^{4}}{8} + \frac{21875 x^{3}}{8} - \frac{65625 x^{2}}{8} + \frac{109375 x}{8} - \frac{78125}{8}) = \sqrt[7]{8 (\frac{x^{7} - 7 \cdot (5 x^{6}) + 21 \cdot (5^{2} x^{5}) - 35 \cdot (5^{3} x^{4}) + 35 \cdot (5^{4} x^{3}) - 21 \cdot (5^{5} x^{2}) + 7 \cdot (5^{6} x) - 1 \cdot 5^{7}}{8})} + 5$

Etapa 5.3.3.2.2

Fatore $x^{7} - 7 \cdot 5 x^{6} + 21 \cdot 5^{2} x^{5} - 35 \cdot 5^{3} x^{4} + 35 \cdot 5^{4} x^{3} - 21 \cdot 5^{5} x^{2} + 7 \cdot 5^{6} x - 1 \cdot 5^{7}$ usando o teorema binomial.

Etapa 5.3.3.3

Combine $8$ e $\frac{{(x - 5)}^{7}}{8}$ .

Etapa 5.3.3.4

Reduza a expressão cancelando os fatores comuns.

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Etapa 5.3.3.4.1

Reduza a expressão $\frac{8 {(x - 5)}^{7}}{8}$ cancelando os fatores comuns.

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Etapa 5.3.3.4.1.1

Cancele o fator comum.

Etapa 5.3.3.4.1.2

Reescreva a expressão.

Etapa 5.3.3.4.2

Divida ${(x - 5)}^{7}$ por $1$ .

Etapa 5.3.3.5

Elimine os termos abaixo do radical, presumindo que sejam números reais.

$f (\frac{x^{7}}{8} - \frac{35 x^{6}}{8} + \frac{525 x^{5}}{8} - \frac{4375 x^{4}}{8} + \frac{21875 x^{3}}{8} - \frac{65625 x^{2}}{8} + \frac{109375 x}{8} - \frac{78125}{8}) = x - 5 + 5$

Etapa 5.3.4

Combine os termos opostos em $x - 5 + 5$ .

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Etapa 5.3.4.1

Some $- 5$ e $5$ .

$f (\frac{x^{7}}{8} - \frac{35 x^{6}}{8} + \frac{525 x^{5}}{8} - \frac{4375 x^{4}}{8} + \frac{21875 x^{3}}{8} - \frac{65625 x^{2}}{8} + \frac{109375 x}{8} - \frac{78125}{8}) = x + 0$

Etapa 5.3.4.2

Some $x$ e $0$ .

$f (\frac{x^{7}}{8} - \frac{35 x^{6}}{8} + \frac{525 x^{5}}{8} - \frac{4375 x^{4}}{8} + \frac{21875 x^{3}}{8} - \frac{65625 x^{2}}{8} + \frac{109375 x}{8} - \frac{78125}{8}) = x$

Etapa 5.4

Como $f^{- 1} (f (x)) = x$ e $f (f^{- 1} (x)) = x$ , então, $f^{- 1} (x) = \frac{x^{7}}{8} - \frac{35 x^{6}}{8} + \frac{525 x^{5}}{8} - \frac{4375 x^{4}}{8} + \frac{21875 x^{3}}{8} - \frac{65625 x^{2}}{8} + \frac{109375 x}{8} - \frac{78125}{8}$ é o inverso de $f (x) = \sqrt[7]{8 x} + 5$ .

$f^{- 1} (x) = \frac{x^{7}}{8} - \frac{35 x^{6}}{8} + \frac{525 x^{5}}{8} - \frac{4375 x^{4}}{8} + \frac{21875 x^{3}}{8} - \frac{65625 x^{2}}{8} + \frac{109375 x}{8} - \frac{78125}{8}$