Álgebra Exemplos

$f (x) = \frac{\sqrt[7]{x} - 8}{3}$

Etapa 1

Escreva $f (x) = \frac{\sqrt[7]{x} - 8}{3}$ como uma equação.

$y = \frac{\sqrt[7]{x} - 8}{3}$

Etapa 2

Alterne as variáveis.

$x = \frac{\sqrt[7]{y} - 8}{3}$

Etapa 3

Resolva $y$ .

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Etapa 3.1

Reescreva a equação como $\frac{\sqrt[7]{y} - 8}{3} = x$ .

$\frac{\sqrt[7]{y} - 8}{3} = x$

Etapa 3.2

Multiplique os dois lados da equação por $3$ .

$3 \frac{\sqrt[7]{y} - 8}{3} = 3 x$

Etapa 3.3

Simplifique o lado esquerdo.

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Etapa 3.3.1

Cancele o fator comum de $3$ .

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Etapa 3.3.1.1

Cancele o fator comum.

$3 \frac{\sqrt[7]{y} - 8}{3} = 3 x$

Etapa 3.3.1.2

Reescreva a expressão.

$\sqrt[7]{y} - 8 = 3 x$

Etapa 3.4

Some $8$ aos dois lados da equação.

$\sqrt[7]{y} = 3 x + 8$

Etapa 3.5

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

${\sqrt[7]{y}}^{7} = {(3 x + 8)}^{7}$

Etapa 3.6

Simplifique cada lado da equação.

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Etapa 3.6.1

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

${(y^{\frac{1}{7}})}^{7} = {(3 x + 8)}^{7}$

Etapa 3.6.2

Simplifique o lado esquerdo.

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Etapa 3.6.2.1

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

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Etapa 3.6.2.1.1

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

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Etapa 3.6.2.1.1.1

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

$y^{\frac{1}{7} \cdot 7} = {(3 x + 8)}^{7}$

Etapa 3.6.2.1.1.2

Cancele o fator comum de $7$ .

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Etapa 3.6.2.1.1.2.1

Cancele o fator comum.

$y^{\frac{1}{7} \cdot 7} = {(3 x + 8)}^{7}$

Etapa 3.6.2.1.1.2.2

Reescreva a expressão.

$y^{1} = {(3 x + 8)}^{7}$

Etapa 3.6.2.1.2

Simplifique.

$y = {(3 x + 8)}^{7}$

Etapa 3.6.3

Simplifique o lado direito.

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Etapa 3.6.3.1

Simplifique ${(3 x + 8)}^{7}$ .

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Etapa 3.6.3.1.1

Use o teorema binomial.

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

Etapa 3.6.3.1.2

Simplifique cada termo.

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Etapa 3.6.3.1.2.1

Aplique a regra do produto a $3 x$ .

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

Etapa 3.6.3.1.2.2

Eleve $3$ à potência de $7$ .

$y = 2187 x^{7} + 7 {(3 x)}^{6} \cdot 8 + 21 {(3 x)}^{5} \cdot 8^{2} + 35 {(3 x)}^{4} \cdot 8^{3} + 35 {(3 x)}^{3} \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Etapa 3.6.3.1.2.3

Aplique a regra do produto a $3 x$ .

$y = 2187 x^{7} + 7 (3^{6} x^{6}) \cdot 8 + 21 {(3 x)}^{5} \cdot 8^{2} + 35 {(3 x)}^{4} \cdot 8^{3} + 35 {(3 x)}^{3} \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Etapa 3.6.3.1.2.4

Eleve $3$ à potência de $6$ .

$y = 2187 x^{7} + 7 (729 x^{6}) \cdot 8 + 21 {(3 x)}^{5} \cdot 8^{2} + 35 {(3 x)}^{4} \cdot 8^{3} + 35 {(3 x)}^{3} \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Etapa 3.6.3.1.2.5

Multiplique $729$ por $7$ .

$y = 2187 x^{7} + 5103 x^{6} \cdot 8 + 21 {(3 x)}^{5} \cdot 8^{2} + 35 {(3 x)}^{4} \cdot 8^{3} + 35 {(3 x)}^{3} \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Etapa 3.6.3.1.2.6

Multiplique $8$ por $5103$ .

$y = 2187 x^{7} + 40824 x^{6} + 21 {(3 x)}^{5} \cdot 8^{2} + 35 {(3 x)}^{4} \cdot 8^{3} + 35 {(3 x)}^{3} \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Etapa 3.6.3.1.2.7

Aplique a regra do produto a $3 x$ .

$y = 2187 x^{7} + 40824 x^{6} + 21 (3^{5} x^{5}) \cdot 8^{2} + 35 {(3 x)}^{4} \cdot 8^{3} + 35 {(3 x)}^{3} \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Etapa 3.6.3.1.2.8

Eleve $3$ à potência de $5$ .

$y = 2187 x^{7} + 40824 x^{6} + 21 (243 x^{5}) \cdot 8^{2} + 35 {(3 x)}^{4} \cdot 8^{3} + 35 {(3 x)}^{3} \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Etapa 3.6.3.1.2.9

Multiplique $243$ por $21$ .

$y = 2187 x^{7} + 40824 x^{6} + 5103 x^{5} \cdot 8^{2} + 35 {(3 x)}^{4} \cdot 8^{3} + 35 {(3 x)}^{3} \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Etapa 3.6.3.1.2.10

Eleve $8$ à potência de $2$ .

$y = 2187 x^{7} + 40824 x^{6} + 5103 x^{5} \cdot 64 + 35 {(3 x)}^{4} \cdot 8^{3} + 35 {(3 x)}^{3} \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Etapa 3.6.3.1.2.11

Multiplique $64$ por $5103$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 35 {(3 x)}^{4} \cdot 8^{3} + 35 {(3 x)}^{3} \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Etapa 3.6.3.1.2.12

Aplique a regra do produto a $3 x$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 35 (3^{4} x^{4}) \cdot 8^{3} + 35 {(3 x)}^{3} \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Etapa 3.6.3.1.2.13

Eleve $3$ à potência de $4$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 35 (81 x^{4}) \cdot 8^{3} + 35 {(3 x)}^{3} \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Etapa 3.6.3.1.2.14

Multiplique $81$ por $35$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 2835 x^{4} \cdot 8^{3} + 35 {(3 x)}^{3} \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Etapa 3.6.3.1.2.15

Eleve $8$ à potência de $3$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 2835 x^{4} \cdot 512 + 35 {(3 x)}^{3} \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Etapa 3.6.3.1.2.16

Multiplique $512$ por $2835$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 35 {(3 x)}^{3} \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Etapa 3.6.3.1.2.17

Aplique a regra do produto a $3 x$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 35 (3^{3} x^{3}) \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Etapa 3.6.3.1.2.18

Eleve $3$ à potência de $3$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 35 (27 x^{3}) \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Etapa 3.6.3.1.2.19

Multiplique $27$ por $35$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 945 x^{3} \cdot 8^{4} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Etapa 3.6.3.1.2.20

Eleve $8$ à potência de $4$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 945 x^{3} \cdot 4096 + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Etapa 3.6.3.1.2.21

Multiplique $4096$ por $945$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 3870720 x^{3} + 21 {(3 x)}^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Etapa 3.6.3.1.2.22

Aplique a regra do produto a $3 x$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 3870720 x^{3} + 21 (3^{2} x^{2}) \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Etapa 3.6.3.1.2.23

Eleve $3$ à potência de $2$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 3870720 x^{3} + 21 (9 x^{2}) \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Etapa 3.6.3.1.2.24

Multiplique $9$ por $21$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 3870720 x^{3} + 189 x^{2} \cdot 8^{5} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Etapa 3.6.3.1.2.25

Eleve $8$ à potência de $5$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 3870720 x^{3} + 189 x^{2} \cdot 32768 + 7 (3 x) \cdot 8^{6} + 8^{7}$

Etapa 3.6.3.1.2.26

Multiplique $32768$ por $189$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 3870720 x^{3} + 6193152 x^{2} + 7 (3 x) \cdot 8^{6} + 8^{7}$

Etapa 3.6.3.1.2.27

Multiplique $3$ por $7$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 3870720 x^{3} + 6193152 x^{2} + 21 x \cdot 8^{6} + 8^{7}$

Etapa 3.6.3.1.2.28

Eleve $8$ à potência de $6$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 3870720 x^{3} + 6193152 x^{2} + 21 x \cdot 262144 + 8^{7}$

Etapa 3.6.3.1.2.29

Multiplique $262144$ por $21$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 3870720 x^{3} + 6193152 x^{2} + 5505024 x + 8^{7}$

Etapa 3.6.3.1.2.30

Eleve $8$ à potência de $7$ .

$y = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 3870720 x^{3} + 6193152 x^{2} + 5505024 x + 2097152$

Etapa 4

Substitua $y$ por $f^{- 1} (x)$ para mostrar a resposta final.

$f^{- 1} (x) = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 3870720 x^{3} + 6193152 x^{2} + 5505024 x + 2097152$

Etapa 5

Verifique se $f^{- 1} (x) = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 3870720 x^{3} + 6193152 x^{2} + 5505024 x + 2097152$ é o inverso de $f (x) = \frac{\sqrt[7]{x} - 8}{3}$ .

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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 $f^{- 1} (\frac{\sqrt[7]{x} - 8}{3})$ substituindo o valor de $f$ em $f^{- 1}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = 2187 {(\frac{\sqrt[7]{x} - 8}{3})}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3

Simplifique cada termo.

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Etapa 5.2.3.1

Aplique a regra do produto a $\frac{\sqrt[7]{x} - 8}{3}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = 2187 (\frac{{(\sqrt[7]{x} - 8)}^{7}}{3^{7}}) + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.2

Eleve $3$ à potência de $7$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = 2187 (\frac{{(\sqrt[7]{x} - 8)}^{7}}{2187}) + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.3

Cancele o fator comum de $2187$ .

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Etapa 5.2.3.3.1

Cancele o fator comum.

Etapa 5.2.3.3.2

Reescreva a expressão.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = {(\sqrt[7]{x} - 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.4

Use o teorema binomial.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = {\sqrt[7]{x}}^{7} + 7 {\sqrt[7]{x}}^{6} \cdot - 8 + 21 {\sqrt[7]{x}}^{5} {(- 8)}^{2} + 35 {\sqrt[7]{x}}^{4} {(- 8)}^{3} + 35 {\sqrt[7]{x}}^{3} {(- 8)}^{4} + 21 {\sqrt[7]{x}}^{2} {(- 8)}^{5} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.5

Simplifique cada termo.

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Etapa 5.2.3.5.1

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

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Etapa 5.2.3.5.1.1

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = {(x^{\frac{1}{7}})}^{7} + 7 {\sqrt[7]{x}}^{6} \cdot - 8 + 21 {\sqrt[7]{x}}^{5} {(- 8)}^{2} + 35 {\sqrt[7]{x}}^{4} {(- 8)}^{3} + 35 {\sqrt[7]{x}}^{3} {(- 8)}^{4} + 21 {\sqrt[7]{x}}^{2} {(- 8)}^{5} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.5.1.2

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x^{\frac{1}{7} \cdot 7} + 7 {\sqrt[7]{x}}^{6} \cdot - 8 + 21 {\sqrt[7]{x}}^{5} {(- 8)}^{2} + 35 {\sqrt[7]{x}}^{4} {(- 8)}^{3} + 35 {\sqrt[7]{x}}^{3} {(- 8)}^{4} + 21 {\sqrt[7]{x}}^{2} {(- 8)}^{5} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.5.1.3

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x^{\frac{7}{7}} + 7 {\sqrt[7]{x}}^{6} \cdot - 8 + 21 {\sqrt[7]{x}}^{5} {(- 8)}^{2} + 35 {\sqrt[7]{x}}^{4} {(- 8)}^{3} + 35 {\sqrt[7]{x}}^{3} {(- 8)}^{4} + 21 {\sqrt[7]{x}}^{2} {(- 8)}^{5} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.5.1.4

Cancele o fator comum de $7$ .

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Etapa 5.2.3.5.1.4.1

Cancele o fator comum.

Etapa 5.2.3.5.1.4.2

Reescreva a expressão.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 7 {\sqrt[7]{x}}^{6} \cdot - 8 + 21 {\sqrt[7]{x}}^{5} {(- 8)}^{2} + 35 {\sqrt[7]{x}}^{4} {(- 8)}^{3} + 35 {\sqrt[7]{x}}^{3} {(- 8)}^{4} + 21 {\sqrt[7]{x}}^{2} {(- 8)}^{5} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.5.1.5

Simplifique.

Etapa 5.2.3.5.2

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 7 \sqrt[7]{x^{6}} \cdot - 8 + 21 {\sqrt[7]{x}}^{5} {(- 8)}^{2} + 35 {\sqrt[7]{x}}^{4} {(- 8)}^{3} + 35 {\sqrt[7]{x}}^{3} {(- 8)}^{4} + 21 {\sqrt[7]{x}}^{2} {(- 8)}^{5} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.5.3

Multiplique $- 8$ por $7$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 21 {\sqrt[7]{x}}^{5} {(- 8)}^{2} + 35 {\sqrt[7]{x}}^{4} {(- 8)}^{3} + 35 {\sqrt[7]{x}}^{3} {(- 8)}^{4} + 21 {\sqrt[7]{x}}^{2} {(- 8)}^{5} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.5.4

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 21 \sqrt[7]{x^{5}} {(- 8)}^{2} + 35 {\sqrt[7]{x}}^{4} {(- 8)}^{3} + 35 {\sqrt[7]{x}}^{3} {(- 8)}^{4} + 21 {\sqrt[7]{x}}^{2} {(- 8)}^{5} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.5.5

Eleve $- 8$ à potência de $2$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 21 \sqrt[7]{x^{5}} \cdot 64 + 35 {\sqrt[7]{x}}^{4} {(- 8)}^{3} + 35 {\sqrt[7]{x}}^{3} {(- 8)}^{4} + 21 {\sqrt[7]{x}}^{2} {(- 8)}^{5} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.5.6

Multiplique $64$ por $21$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} + 35 {\sqrt[7]{x}}^{4} {(- 8)}^{3} + 35 {\sqrt[7]{x}}^{3} {(- 8)}^{4} + 21 {\sqrt[7]{x}}^{2} {(- 8)}^{5} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.5.7

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} + 35 \sqrt[7]{x^{4}} {(- 8)}^{3} + 35 {\sqrt[7]{x}}^{3} {(- 8)}^{4} + 21 {\sqrt[7]{x}}^{2} {(- 8)}^{5} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.5.8

Eleve $- 8$ à potência de $3$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} + 35 \sqrt[7]{x^{4}} \cdot - 512 + 35 {\sqrt[7]{x}}^{3} {(- 8)}^{4} + 21 {\sqrt[7]{x}}^{2} {(- 8)}^{5} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.5.9

Multiplique $- 512$ por $35$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 35 {\sqrt[7]{x}}^{3} {(- 8)}^{4} + 21 {\sqrt[7]{x}}^{2} {(- 8)}^{5} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.5.10

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 35 \sqrt[7]{x^{3}} {(- 8)}^{4} + 21 {\sqrt[7]{x}}^{2} {(- 8)}^{5} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.5.11

Eleve $- 8$ à potência de $4$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 35 \sqrt[7]{x^{3}} \cdot 4096 + 21 {\sqrt[7]{x}}^{2} {(- 8)}^{5} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.5.12

Multiplique $4096$ por $35$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} + 21 {\sqrt[7]{x}}^{2} {(- 8)}^{5} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.5.13

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} + 21 \sqrt[7]{x^{2}} {(- 8)}^{5} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.5.14

Eleve $- 8$ à potência de $5$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} + 21 \sqrt[7]{x^{2}} \cdot - 32768 + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.5.15

Multiplique $- 32768$ por $21$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 7 \sqrt[7]{x} {(- 8)}^{6} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.5.16

Eleve $- 8$ à potência de $6$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 7 \sqrt[7]{x} \cdot 262144 + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.5.17

Multiplique $262144$ por $7$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} + {(- 8)}^{7} + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.5.18

Eleve $- 8$ à potência de $7$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 40824 {(\frac{\sqrt[7]{x} - 8}{3})}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.6

Aplique a regra do produto a $\frac{\sqrt[7]{x} - 8}{3}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 40824 (\frac{{(\sqrt[7]{x} - 8)}^{6}}{3^{6}}) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.7

Eleve $3$ à potência de $6$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 40824 (\frac{{(\sqrt[7]{x} - 8)}^{6}}{729}) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.8

Cancele o fator comum de $729$ .

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Etapa 5.2.3.8.1

Fatore $729$ de $40824$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 729 (56) (\frac{{(\sqrt[7]{x} - 8)}^{6}}{729}) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.8.2

Cancele o fator comum.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 729 \cdot (56 (\frac{{(\sqrt[7]{x} - 8)}^{6}}{729})) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.8.3

Reescreva a expressão.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 {(\sqrt[7]{x} - 8)}^{6} + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.9

Use o teorema binomial.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 ({\sqrt[7]{x}}^{6} + 6 {\sqrt[7]{x}}^{5} \cdot - 8 + 15 {\sqrt[7]{x}}^{4} {(- 8)}^{2} + 20 {\sqrt[7]{x}}^{3} {(- 8)}^{3} + 15 {\sqrt[7]{x}}^{2} {(- 8)}^{4} + 6 \sqrt[7]{x} {(- 8)}^{5} + {(- 8)}^{6}) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.10

Simplifique cada termo.

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Etapa 5.2.3.10.1

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 (\sqrt[7]{x^{6}} + 6 {\sqrt[7]{x}}^{5} \cdot - 8 + 15 {\sqrt[7]{x}}^{4} {(- 8)}^{2} + 20 {\sqrt[7]{x}}^{3} {(- 8)}^{3} + 15 {\sqrt[7]{x}}^{2} {(- 8)}^{4} + 6 \sqrt[7]{x} {(- 8)}^{5} + {(- 8)}^{6}) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.10.2

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 (\sqrt[7]{x^{6}} + 6 \sqrt[7]{x^{5}} \cdot - 8 + 15 {\sqrt[7]{x}}^{4} {(- 8)}^{2} + 20 {\sqrt[7]{x}}^{3} {(- 8)}^{3} + 15 {\sqrt[7]{x}}^{2} {(- 8)}^{4} + 6 \sqrt[7]{x} {(- 8)}^{5} + {(- 8)}^{6}) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.10.3

Multiplique $- 8$ por $6$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 (\sqrt[7]{x^{6}} - 48 \sqrt[7]{x^{5}} + 15 {\sqrt[7]{x}}^{4} {(- 8)}^{2} + 20 {\sqrt[7]{x}}^{3} {(- 8)}^{3} + 15 {\sqrt[7]{x}}^{2} {(- 8)}^{4} + 6 \sqrt[7]{x} {(- 8)}^{5} + {(- 8)}^{6}) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.10.4

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 (\sqrt[7]{x^{6}} - 48 \sqrt[7]{x^{5}} + 15 \sqrt[7]{x^{4}} {(- 8)}^{2} + 20 {\sqrt[7]{x}}^{3} {(- 8)}^{3} + 15 {\sqrt[7]{x}}^{2} {(- 8)}^{4} + 6 \sqrt[7]{x} {(- 8)}^{5} + {(- 8)}^{6}) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.10.5

Eleve $- 8$ à potência de $2$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 (\sqrt[7]{x^{6}} - 48 \sqrt[7]{x^{5}} + 15 \sqrt[7]{x^{4}} \cdot 64 + 20 {\sqrt[7]{x}}^{3} {(- 8)}^{3} + 15 {\sqrt[7]{x}}^{2} {(- 8)}^{4} + 6 \sqrt[7]{x} {(- 8)}^{5} + {(- 8)}^{6}) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.10.6

Multiplique $64$ por $15$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 (\sqrt[7]{x^{6}} - 48 \sqrt[7]{x^{5}} + 960 \sqrt[7]{x^{4}} + 20 {\sqrt[7]{x}}^{3} {(- 8)}^{3} + 15 {\sqrt[7]{x}}^{2} {(- 8)}^{4} + 6 \sqrt[7]{x} {(- 8)}^{5} + {(- 8)}^{6}) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.10.7

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 (\sqrt[7]{x^{6}} - 48 \sqrt[7]{x^{5}} + 960 \sqrt[7]{x^{4}} + 20 \sqrt[7]{x^{3}} {(- 8)}^{3} + 15 {\sqrt[7]{x}}^{2} {(- 8)}^{4} + 6 \sqrt[7]{x} {(- 8)}^{5} + {(- 8)}^{6}) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.10.8

Eleve $- 8$ à potência de $3$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 (\sqrt[7]{x^{6}} - 48 \sqrt[7]{x^{5}} + 960 \sqrt[7]{x^{4}} + 20 \sqrt[7]{x^{3}} \cdot - 512 + 15 {\sqrt[7]{x}}^{2} {(- 8)}^{4} + 6 \sqrt[7]{x} {(- 8)}^{5} + {(- 8)}^{6}) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.10.9

Multiplique $- 512$ por $20$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 (\sqrt[7]{x^{6}} - 48 \sqrt[7]{x^{5}} + 960 \sqrt[7]{x^{4}} - 10240 \sqrt[7]{x^{3}} + 15 {\sqrt[7]{x}}^{2} {(- 8)}^{4} + 6 \sqrt[7]{x} {(- 8)}^{5} + {(- 8)}^{6}) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.10.10

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 (\sqrt[7]{x^{6}} - 48 \sqrt[7]{x^{5}} + 960 \sqrt[7]{x^{4}} - 10240 \sqrt[7]{x^{3}} + 15 \sqrt[7]{x^{2}} {(- 8)}^{4} + 6 \sqrt[7]{x} {(- 8)}^{5} + {(- 8)}^{6}) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.10.11

Eleve $- 8$ à potência de $4$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 (\sqrt[7]{x^{6}} - 48 \sqrt[7]{x^{5}} + 960 \sqrt[7]{x^{4}} - 10240 \sqrt[7]{x^{3}} + 15 \sqrt[7]{x^{2}} \cdot 4096 + 6 \sqrt[7]{x} {(- 8)}^{5} + {(- 8)}^{6}) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.10.12

Multiplique $4096$ por $15$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 (\sqrt[7]{x^{6}} - 48 \sqrt[7]{x^{5}} + 960 \sqrt[7]{x^{4}} - 10240 \sqrt[7]{x^{3}} + 61440 \sqrt[7]{x^{2}} + 6 \sqrt[7]{x} {(- 8)}^{5} + {(- 8)}^{6}) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.10.13

Eleve $- 8$ à potência de $5$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 (\sqrt[7]{x^{6}} - 48 \sqrt[7]{x^{5}} + 960 \sqrt[7]{x^{4}} - 10240 \sqrt[7]{x^{3}} + 61440 \sqrt[7]{x^{2}} + 6 \sqrt[7]{x} \cdot - 32768 + {(- 8)}^{6}) + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.10.14

Multiplique $- 32768$ por $6$ .

Etapa 5.2.3.10.15

Eleve $- 8$ à potência de $6$ .

Etapa 5.2.3.11

Aplique a propriedade distributiva.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} + 56 (- 48 \sqrt[7]{x^{5}}) + 56 (960 \sqrt[7]{x^{4}}) + 56 (- 10240 \sqrt[7]{x^{3}}) + 56 (61440 \sqrt[7]{x^{2}}) + 56 (- 196608 \sqrt[7]{x}) + 56 \cdot 262144 + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.12

Simplifique.

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Etapa 5.2.3.12.1

Multiplique $- 48$ por $56$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 56 (960 \sqrt[7]{x^{4}}) + 56 (- 10240 \sqrt[7]{x^{3}}) + 56 (61440 \sqrt[7]{x^{2}}) + 56 (- 196608 \sqrt[7]{x}) + 56 \cdot 262144 + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.12.2

Multiplique $960$ por $56$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} + 56 (- 10240 \sqrt[7]{x^{3}}) + 56 (61440 \sqrt[7]{x^{2}}) + 56 (- 196608 \sqrt[7]{x}) + 56 \cdot 262144 + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.12.3

Multiplique $- 10240$ por $56$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 56 (61440 \sqrt[7]{x^{2}}) + 56 (- 196608 \sqrt[7]{x}) + 56 \cdot 262144 + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.12.4

Multiplique $61440$ por $56$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} + 56 (- 196608 \sqrt[7]{x}) + 56 \cdot 262144 + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.12.5

Multiplique $- 196608$ por $56$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 56 \cdot 262144 + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.12.6

Multiplique $56$ por $262144$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 326592 {(\frac{\sqrt[7]{x} - 8}{3})}^{5} + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.13

Aplique a regra do produto a $\frac{\sqrt[7]{x} - 8}{3}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 326592 (\frac{{(\sqrt[7]{x} - 8)}^{5}}{3^{5}}) + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.14

Eleve $3$ à potência de $5$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 326592 (\frac{{(\sqrt[7]{x} - 8)}^{5}}{243}) + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.15

Cancele o fator comum de $243$ .

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Etapa 5.2.3.15.1

Fatore $243$ de $326592$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 243 (1344) (\frac{{(\sqrt[7]{x} - 8)}^{5}}{243}) + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.15.2

Cancele o fator comum.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 243 \cdot (1344 (\frac{{(\sqrt[7]{x} - 8)}^{5}}{243})) + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.15.3

Reescreva a expressão.

Etapa 5.2.3.16

Use o teorema binomial.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 ({\sqrt[7]{x}}^{5} + 5 {\sqrt[7]{x}}^{4} \cdot - 8 + 10 {\sqrt[7]{x}}^{3} {(- 8)}^{2} + 10 {\sqrt[7]{x}}^{2} {(- 8)}^{3} + 5 \sqrt[7]{x} {(- 8)}^{4} + {(- 8)}^{5}) + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.17

Simplifique cada termo.

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Etapa 5.2.3.17.1

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 (\sqrt[7]{x^{5}} + 5 {\sqrt[7]{x}}^{4} \cdot - 8 + 10 {\sqrt[7]{x}}^{3} {(- 8)}^{2} + 10 {\sqrt[7]{x}}^{2} {(- 8)}^{3} + 5 \sqrt[7]{x} {(- 8)}^{4} + {(- 8)}^{5}) + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.17.2

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 (\sqrt[7]{x^{5}} + 5 \sqrt[7]{x^{4}} \cdot - 8 + 10 {\sqrt[7]{x}}^{3} {(- 8)}^{2} + 10 {\sqrt[7]{x}}^{2} {(- 8)}^{3} + 5 \sqrt[7]{x} {(- 8)}^{4} + {(- 8)}^{5}) + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.17.3

Multiplique $- 8$ por $5$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 (\sqrt[7]{x^{5}} - 40 \sqrt[7]{x^{4}} + 10 {\sqrt[7]{x}}^{3} {(- 8)}^{2} + 10 {\sqrt[7]{x}}^{2} {(- 8)}^{3} + 5 \sqrt[7]{x} {(- 8)}^{4} + {(- 8)}^{5}) + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.17.4

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 (\sqrt[7]{x^{5}} - 40 \sqrt[7]{x^{4}} + 10 \sqrt[7]{x^{3}} {(- 8)}^{2} + 10 {\sqrt[7]{x}}^{2} {(- 8)}^{3} + 5 \sqrt[7]{x} {(- 8)}^{4} + {(- 8)}^{5}) + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.17.5

Eleve $- 8$ à potência de $2$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 (\sqrt[7]{x^{5}} - 40 \sqrt[7]{x^{4}} + 10 \sqrt[7]{x^{3}} \cdot 64 + 10 {\sqrt[7]{x}}^{2} {(- 8)}^{3} + 5 \sqrt[7]{x} {(- 8)}^{4} + {(- 8)}^{5}) + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.17.6

Multiplique $64$ por $10$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 (\sqrt[7]{x^{5}} - 40 \sqrt[7]{x^{4}} + 640 \sqrt[7]{x^{3}} + 10 {\sqrt[7]{x}}^{2} {(- 8)}^{3} + 5 \sqrt[7]{x} {(- 8)}^{4} + {(- 8)}^{5}) + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.17.7

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 (\sqrt[7]{x^{5}} - 40 \sqrt[7]{x^{4}} + 640 \sqrt[7]{x^{3}} + 10 \sqrt[7]{x^{2}} {(- 8)}^{3} + 5 \sqrt[7]{x} {(- 8)}^{4} + {(- 8)}^{5}) + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.17.8

Eleve $- 8$ à potência de $3$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 (\sqrt[7]{x^{5}} - 40 \sqrt[7]{x^{4}} + 640 \sqrt[7]{x^{3}} + 10 \sqrt[7]{x^{2}} \cdot - 512 + 5 \sqrt[7]{x} {(- 8)}^{4} + {(- 8)}^{5}) + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.17.9

Multiplique $- 512$ por $10$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 (\sqrt[7]{x^{5}} - 40 \sqrt[7]{x^{4}} + 640 \sqrt[7]{x^{3}} - 5120 \sqrt[7]{x^{2}} + 5 \sqrt[7]{x} {(- 8)}^{4} + {(- 8)}^{5}) + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.17.10

Eleve $- 8$ à potência de $4$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 (\sqrt[7]{x^{5}} - 40 \sqrt[7]{x^{4}} + 640 \sqrt[7]{x^{3}} - 5120 \sqrt[7]{x^{2}} + 5 \sqrt[7]{x} \cdot 4096 + {(- 8)}^{5}) + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.17.11

Multiplique $4096$ por $5$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 (\sqrt[7]{x^{5}} - 40 \sqrt[7]{x^{4}} + 640 \sqrt[7]{x^{3}} - 5120 \sqrt[7]{x^{2}} + 20480 \sqrt[7]{x} + {(- 8)}^{5}) + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.17.12

Eleve $- 8$ à potência de $5$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 (\sqrt[7]{x^{5}} - 40 \sqrt[7]{x^{4}} + 640 \sqrt[7]{x^{3}} - 5120 \sqrt[7]{x^{2}} + 20480 \sqrt[7]{x} - 32768) + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.18

Aplique a propriedade distributiva.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 1344 (- 40 \sqrt[7]{x^{4}}) + 1344 (640 \sqrt[7]{x^{3}}) + 1344 (- 5120 \sqrt[7]{x^{2}}) + 1344 (20480 \sqrt[7]{x}) + 1344 \cdot - 32768 + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.19

Simplifique.

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Etapa 5.2.3.19.1

Multiplique $- 40$ por $1344$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 1344 (640 \sqrt[7]{x^{3}}) + 1344 (- 5120 \sqrt[7]{x^{2}}) + 1344 (20480 \sqrt[7]{x}) + 1344 \cdot - 32768 + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.19.2

Multiplique $640$ por $1344$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} + 1344 (- 5120 \sqrt[7]{x^{2}}) + 1344 (20480 \sqrt[7]{x}) + 1344 \cdot - 32768 + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.19.3

Multiplique $- 5120$ por $1344$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 1344 (20480 \sqrt[7]{x}) + 1344 \cdot - 32768 + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.19.4

Multiplique $20480$ por $1344$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} + 1344 \cdot - 32768 + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.19.5

Multiplique $1344$ por $- 32768$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 1451520 {(\frac{\sqrt[7]{x} - 8}{3})}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.20

Aplique a regra do produto a $\frac{\sqrt[7]{x} - 8}{3}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 1451520 (\frac{{(\sqrt[7]{x} - 8)}^{4}}{3^{4}}) + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.21

Eleve $3$ à potência de $4$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 1451520 (\frac{{(\sqrt[7]{x} - 8)}^{4}}{81}) + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.22

Cancele o fator comum de $81$ .

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Etapa 5.2.3.22.1

Fatore $81$ de $1451520$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 81 (17920) (\frac{{(\sqrt[7]{x} - 8)}^{4}}{81}) + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.22.2

Cancele o fator comum.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 81 \cdot (17920 (\frac{{(\sqrt[7]{x} - 8)}^{4}}{81})) + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.22.3

Reescreva a expressão.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 {(\sqrt[7]{x} - 8)}^{4} + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.23

Use o teorema binomial.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 ({\sqrt[7]{x}}^{4} + 4 {\sqrt[7]{x}}^{3} \cdot - 8 + 6 {\sqrt[7]{x}}^{2} {(- 8)}^{2} + 4 \sqrt[7]{x} {(- 8)}^{3} + {(- 8)}^{4}) + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.24

Simplifique cada termo.

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Etapa 5.2.3.24.1

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 (\sqrt[7]{x^{4}} + 4 {\sqrt[7]{x}}^{3} \cdot - 8 + 6 {\sqrt[7]{x}}^{2} {(- 8)}^{2} + 4 \sqrt[7]{x} {(- 8)}^{3} + {(- 8)}^{4}) + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.24.2

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 (\sqrt[7]{x^{4}} + 4 \sqrt[7]{x^{3}} \cdot - 8 + 6 {\sqrt[7]{x}}^{2} {(- 8)}^{2} + 4 \sqrt[7]{x} {(- 8)}^{3} + {(- 8)}^{4}) + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.24.3

Multiplique $- 8$ por $4$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 (\sqrt[7]{x^{4}} - 32 \sqrt[7]{x^{3}} + 6 {\sqrt[7]{x}}^{2} {(- 8)}^{2} + 4 \sqrt[7]{x} {(- 8)}^{3} + {(- 8)}^{4}) + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.24.4

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 (\sqrt[7]{x^{4}} - 32 \sqrt[7]{x^{3}} + 6 \sqrt[7]{x^{2}} {(- 8)}^{2} + 4 \sqrt[7]{x} {(- 8)}^{3} + {(- 8)}^{4}) + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.24.5

Eleve $- 8$ à potência de $2$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 (\sqrt[7]{x^{4}} - 32 \sqrt[7]{x^{3}} + 6 \sqrt[7]{x^{2}} \cdot 64 + 4 \sqrt[7]{x} {(- 8)}^{3} + {(- 8)}^{4}) + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.24.6

Multiplique $64$ por $6$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 (\sqrt[7]{x^{4}} - 32 \sqrt[7]{x^{3}} + 384 \sqrt[7]{x^{2}} + 4 \sqrt[7]{x} {(- 8)}^{3} + {(- 8)}^{4}) + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.24.7

Eleve $- 8$ à potência de $3$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 (\sqrt[7]{x^{4}} - 32 \sqrt[7]{x^{3}} + 384 \sqrt[7]{x^{2}} + 4 \sqrt[7]{x} \cdot - 512 + {(- 8)}^{4}) + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.24.8

Multiplique $- 512$ por $4$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 (\sqrt[7]{x^{4}} - 32 \sqrt[7]{x^{3}} + 384 \sqrt[7]{x^{2}} - 2048 \sqrt[7]{x} + {(- 8)}^{4}) + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.24.9

Eleve $- 8$ à potência de $4$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 (\sqrt[7]{x^{4}} - 32 \sqrt[7]{x^{3}} + 384 \sqrt[7]{x^{2}} - 2048 \sqrt[7]{x} + 4096) + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.25

Aplique a propriedade distributiva.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} + 17920 (- 32 \sqrt[7]{x^{3}}) + 17920 (384 \sqrt[7]{x^{2}}) + 17920 (- 2048 \sqrt[7]{x}) + 17920 \cdot 4096 + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.26

Simplifique.

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Etapa 5.2.3.26.1

Multiplique $- 32$ por $17920$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 17920 (384 \sqrt[7]{x^{2}}) + 17920 (- 2048 \sqrt[7]{x}) + 17920 \cdot 4096 + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.26.2

Multiplique $384$ por $17920$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} + 17920 (- 2048 \sqrt[7]{x}) + 17920 \cdot 4096 + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.26.3

Multiplique $- 2048$ por $17920$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 17920 \cdot 4096 + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.26.4

Multiplique $17920$ por $4096$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 3870720 {(\frac{\sqrt[7]{x} - 8}{3})}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.27

Aplique a regra do produto a $\frac{\sqrt[7]{x} - 8}{3}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 3870720 (\frac{{(\sqrt[7]{x} - 8)}^{3}}{3^{3}}) + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.28

Eleve $3$ à potência de $3$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 3870720 (\frac{{(\sqrt[7]{x} - 8)}^{3}}{27}) + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.29

Cancele o fator comum de $27$ .

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Etapa 5.2.3.29.1

Fatore $27$ de $3870720$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 27 (143360) (\frac{{(\sqrt[7]{x} - 8)}^{3}}{27}) + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.29.2

Cancele o fator comum.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 27 \cdot (143360 (\frac{{(\sqrt[7]{x} - 8)}^{3}}{27})) + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.29.3

Reescreva a expressão.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 {(\sqrt[7]{x} - 8)}^{3} + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.30

Use o teorema binomial.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 ({\sqrt[7]{x}}^{3} + 3 {\sqrt[7]{x}}^{2} \cdot - 8 + 3 \sqrt[7]{x} {(- 8)}^{2} + {(- 8)}^{3}) + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.31

Simplifique cada termo.

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Etapa 5.2.3.31.1

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 (\sqrt[7]{x^{3}} + 3 {\sqrt[7]{x}}^{2} \cdot - 8 + 3 \sqrt[7]{x} {(- 8)}^{2} + {(- 8)}^{3}) + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.31.2

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 (\sqrt[7]{x^{3}} + 3 \sqrt[7]{x^{2}} \cdot - 8 + 3 \sqrt[7]{x} {(- 8)}^{2} + {(- 8)}^{3}) + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.31.3

Multiplique $- 8$ por $3$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 (\sqrt[7]{x^{3}} - 24 \sqrt[7]{x^{2}} + 3 \sqrt[7]{x} {(- 8)}^{2} + {(- 8)}^{3}) + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.31.4

Eleve $- 8$ à potência de $2$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 (\sqrt[7]{x^{3}} - 24 \sqrt[7]{x^{2}} + 3 \sqrt[7]{x} \cdot 64 + {(- 8)}^{3}) + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.31.5

Multiplique $64$ por $3$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 (\sqrt[7]{x^{3}} - 24 \sqrt[7]{x^{2}} + 192 \sqrt[7]{x} + {(- 8)}^{3}) + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.31.6

Eleve $- 8$ à potência de $3$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 (\sqrt[7]{x^{3}} - 24 \sqrt[7]{x^{2}} + 192 \sqrt[7]{x} - 512) + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.32

Aplique a propriedade distributiva.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} + 143360 (- 24 \sqrt[7]{x^{2}}) + 143360 (192 \sqrt[7]{x}) + 143360 \cdot - 512 + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.33

Simplifique.

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Etapa 5.2.3.33.1

Multiplique $- 24$ por $143360$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 143360 (192 \sqrt[7]{x}) + 143360 \cdot - 512 + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.33.2

Multiplique $192$ por $143360$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} + 143360 \cdot - 512 + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.33.3

Multiplique $143360$ por $- 512$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 6193152 {(\frac{\sqrt[7]{x} - 8}{3})}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.34

Aplique a regra do produto a $\frac{\sqrt[7]{x} - 8}{3}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 6193152 (\frac{{(\sqrt[7]{x} - 8)}^{2}}{3^{2}}) + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.35

Eleve $3$ à potência de $2$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 6193152 (\frac{{(\sqrt[7]{x} - 8)}^{2}}{9}) + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.36

Cancele o fator comum de $9$ .

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Etapa 5.2.3.36.1

Fatore $9$ de $6193152$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 9 (688128) (\frac{{(\sqrt[7]{x} - 8)}^{2}}{9}) + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.36.2

Cancele o fator comum.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 9 \cdot (688128 (\frac{{(\sqrt[7]{x} - 8)}^{2}}{9})) + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.36.3

Reescreva a expressão.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 {(\sqrt[7]{x} - 8)}^{2} + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.37

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 ((\sqrt[7]{x} - 8) (\sqrt[7]{x} - 8)) + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.38

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

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Etapa 5.2.3.38.1

Aplique a propriedade distributiva.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 (\sqrt[7]{x} (\sqrt[7]{x} - 8) - 8 (\sqrt[7]{x} - 8)) + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.38.2

Aplique a propriedade distributiva.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 (\sqrt[7]{x} \sqrt[7]{x} + \sqrt[7]{x} \cdot - 8 - 8 (\sqrt[7]{x} - 8)) + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.38.3

Aplique a propriedade distributiva.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 (\sqrt[7]{x} \sqrt[7]{x} + \sqrt[7]{x} \cdot - 8 - 8 \sqrt[7]{x} - 8 \cdot - 8) + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.39

Simplifique e combine termos semelhantes.

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Etapa 5.2.3.39.1

Simplifique cada termo.

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Etapa 5.2.3.39.1.1

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

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Etapa 5.2.3.39.1.1.1

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 (\sqrt[7]{x} \sqrt[7]{x} + \sqrt[7]{x} \cdot - 8 - 8 \sqrt[7]{x} - 8 \cdot - 8) + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.39.1.1.2

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 (\sqrt[7]{x} \sqrt[7]{x} + \sqrt[7]{x} \cdot - 8 - 8 \sqrt[7]{x} - 8 \cdot - 8) + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.39.1.1.3

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 ({\sqrt[7]{x}}^{1 + 1} + \sqrt[7]{x} \cdot - 8 - 8 \sqrt[7]{x} - 8 \cdot - 8) + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.39.1.1.4

Some $1$ e $1$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 ({\sqrt[7]{x}}^{2} + \sqrt[7]{x} \cdot - 8 - 8 \sqrt[7]{x} - 8 \cdot - 8) + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.39.1.2

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 (\sqrt[7]{x^{2}} + \sqrt[7]{x} \cdot - 8 - 8 \sqrt[7]{x} - 8 \cdot - 8) + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.39.1.3

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 (\sqrt[7]{x^{2}} - 8 \cdot \sqrt[7]{x} - 8 \sqrt[7]{x} - 8 \cdot - 8) + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.39.1.4

Multiplique $- 8$ por $- 8$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 (\sqrt[7]{x^{2}} - 8 \sqrt[7]{x} - 8 \sqrt[7]{x} + 64) + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.39.2

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

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 (\sqrt[7]{x^{2}} - 16 \sqrt[7]{x} + 64) + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.40

Aplique a propriedade distributiva.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} + 688128 (- 16 \sqrt[7]{x}) + 688128 \cdot 64 + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.41

Simplifique.

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Etapa 5.2.3.41.1

Multiplique $- 16$ por $688128$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 688128 \cdot 64 + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.41.2

Multiplique $688128$ por $64$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 5505024 (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.42

Cancele o fator comum de $3$ .

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Etapa 5.2.3.42.1

Fatore $3$ de $5505024$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 3 (1835008) (\frac{\sqrt[7]{x} - 8}{3}) + 2097152$

Etapa 5.2.3.42.2

Cancele o fator comum.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 3 \cdot (1835008 (\frac{\sqrt[7]{x} - 8}{3})) + 2097152$

Etapa 5.2.3.42.3

Reescreva a expressão.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 (\sqrt[7]{x} - 8) + 2097152$

Etapa 5.2.3.43

Aplique a propriedade distributiva.

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 \sqrt[7]{x} + 1835008 \cdot - 8 + 2097152$

Etapa 5.2.3.44

Multiplique $1835008$ por $- 8$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 \sqrt[7]{x} - 14680064 + 2097152$

Etapa 5.2.4

Simplifique somando os termos.

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Etapa 5.2.4.1

Combine os termos opostos em $x - 56 \sqrt[7]{x^{6}} + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 + 56 \sqrt[7]{x^{6}} - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 \sqrt[7]{x} - 14680064 + 2097152$ .

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Etapa 5.2.4.1.1

Some $- 56 \sqrt[7]{x^{6}}$ e $56 \sqrt[7]{x^{6}}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 0 + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 \sqrt[7]{x} - 14680064 + 2097152$

Etapa 5.2.4.1.2

Some $x$ e $0$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} + 53760 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} - 53760 \sqrt[7]{x^{4}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 \sqrt[7]{x} - 14680064 + 2097152$

Etapa 5.2.4.1.3

Subtraia $53760 \sqrt[7]{x^{4}}$ de $53760 \sqrt[7]{x^{4}}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} + 0 - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 \sqrt[7]{x} - 14680064 + 2097152$

Etapa 5.2.4.1.4

Some $x + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}}$ e $0$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} - 17920 \sqrt[7]{x^{4}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 + 17920 \sqrt[7]{x^{4}} - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 \sqrt[7]{x} - 14680064 + 2097152$

Etapa 5.2.4.1.5

Some $- 17920 \sqrt[7]{x^{4}}$ e $17920 \sqrt[7]{x^{4}}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} + 0 + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 \sqrt[7]{x} - 14680064 + 2097152$

Etapa 5.2.4.1.6

Some $x + 1344 \sqrt[7]{x^{5}}$ e $0$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} - 6881280 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 44040192 - 573440 \sqrt[7]{x^{3}} + 6881280 \sqrt[7]{x^{2}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 \sqrt[7]{x} - 14680064 + 2097152$

Etapa 5.2.4.1.7

Some $- 6881280 \sqrt[7]{x^{2}}$ e $6881280 \sqrt[7]{x^{2}}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 0 + 27525120 \sqrt[7]{x} - 44040192 - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 \sqrt[7]{x} - 14680064 + 2097152$

Etapa 5.2.4.1.8

Some $x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}}$ e $0$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} + 3440640 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 44040192 - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} - 3440640 \sqrt[7]{x^{2}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 \sqrt[7]{x} - 14680064 + 2097152$

Etapa 5.2.4.1.9

Subtraia $3440640 \sqrt[7]{x^{2}}$ de $3440640 \sqrt[7]{x^{2}}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} + 0 - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 44040192 - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 \sqrt[7]{x} - 14680064 + 2097152$

Etapa 5.2.4.1.10

Some $x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}}$ e $0$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 44040192 - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 73400320 + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 73400320 + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 \sqrt[7]{x} - 14680064 + 2097152$

Etapa 5.2.4.1.11

Subtraia $73400320$ de $73400320$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 44040192 - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 0 + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 \sqrt[7]{x} - 14680064 + 2097152$

Etapa 5.2.4.1.12

Some $x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 44040192 - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x}$ e $0$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} - 688128 \sqrt[7]{x^{2}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 44040192 - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} + 688128 \sqrt[7]{x^{2}} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 \sqrt[7]{x} - 14680064 + 2097152$

Etapa 5.2.4.1.13

Some $- 688128 \sqrt[7]{x^{2}}$ e $688128 \sqrt[7]{x^{2}}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} + 0 + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 44040192 - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 \sqrt[7]{x} - 14680064 + 2097152$

Etapa 5.2.4.1.14

Some $x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}}$ e $0$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 44040192 - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 44040192 + 1835008 \sqrt[7]{x} - 14680064 + 2097152$

Etapa 5.2.4.1.15

Some $- 44040192$ e $44040192$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} + 0 - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x} - 14680064 + 2097152$

Etapa 5.2.4.1.16

Some $x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x}$ e $0$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x} + 14680064 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x} - 14680064 + 2097152$

Etapa 5.2.4.1.17

Subtraia $14680064$ de $14680064$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x} + 0 + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x} + 2097152$

Etapa 5.2.4.1.18

Some $x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x}$ e $0$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x} - 2097152 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x} + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x} + 2097152$

Etapa 5.2.4.1.19

Some $- 2097152$ e $2097152$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x} + 0 - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x} + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$

Etapa 5.2.4.1.20

Some $x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x}$ e $0$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x} - 2688 \sqrt[7]{x^{5}} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x} + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$

Etapa 5.2.4.2

Subtraia $2688 \sqrt[7]{x^{5}}$ de $1344 \sqrt[7]{x^{5}}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x} + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$

Etapa 5.2.4.3

Combine os termos opostos em $x - 1344 \sqrt[7]{x^{5}} + 143360 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x} + 1344 \sqrt[7]{x^{5}} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$ .

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Etapa 5.2.4.3.1

Some $- 1344 \sqrt[7]{x^{5}}$ e $1344 \sqrt[7]{x^{5}}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 0 + 143360 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$

Etapa 5.2.4.3.2

Some $x$ e $0$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 143360 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x} - 573440 \sqrt[7]{x^{3}} - 11010048 \sqrt[7]{x} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$

Etapa 5.2.4.4

Subtraia $573440 \sqrt[7]{x^{3}}$ de $143360 \sqrt[7]{x^{3}}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 430080 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 860160 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$

Etapa 5.2.4.5

Some $- 430080 \sqrt[7]{x^{3}}$ e $860160 \sqrt[7]{x^{3}}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 430080 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 27525120 \sqrt[7]{x} - 573440 \sqrt[7]{x^{3}} - 36700160 \sqrt[7]{x} + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$

Etapa 5.2.4.6

Subtraia $573440 \sqrt[7]{x^{3}}$ de $430080 \sqrt[7]{x^{3}}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 143360 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 27525120 \sqrt[7]{x} - 36700160 \sqrt[7]{x} + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$

Etapa 5.2.4.7

Combine os termos opostos em $x - 143360 \sqrt[7]{x^{3}} + 1835008 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 27525120 \sqrt[7]{x} - 36700160 \sqrt[7]{x} + 143360 \sqrt[7]{x^{3}} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$ .

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Etapa 5.2.4.7.1

Some $- 143360 \sqrt[7]{x^{3}}$ e $143360 \sqrt[7]{x^{3}}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 0 + 1835008 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 27525120 \sqrt[7]{x} - 36700160 \sqrt[7]{x} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$

Etapa 5.2.4.7.2

Some $x$ e $0$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 1835008 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 27525120 \sqrt[7]{x} - 36700160 \sqrt[7]{x} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$

Etapa 5.2.4.8

Subtraia $11010048 \sqrt[7]{x}$ de $1835008 \sqrt[7]{x}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 9175040 \sqrt[7]{x} + 27525120 \sqrt[7]{x} - 36700160 \sqrt[7]{x} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$

Etapa 5.2.4.9

Some $- 9175040 \sqrt[7]{x}$ e $27525120 \sqrt[7]{x}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 18350080 \sqrt[7]{x} - 36700160 \sqrt[7]{x} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$

Etapa 5.2.4.10

Subtraia $36700160 \sqrt[7]{x}$ de $18350080 \sqrt[7]{x}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 18350080 \sqrt[7]{x} + 27525120 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$

Etapa 5.2.4.11

Some $- 18350080 \sqrt[7]{x}$ e $27525120 \sqrt[7]{x}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 9175040 \sqrt[7]{x} - 11010048 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$

Etapa 5.2.4.12

Subtraia $11010048 \sqrt[7]{x}$ de $9175040 \sqrt[7]{x}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x - 1835008 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$

Etapa 5.2.4.13

Combine os termos opostos em $x - 1835008 \sqrt[7]{x} + 1835008 \sqrt[7]{x}$ .

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Etapa 5.2.4.13.1

Some $- 1835008 \sqrt[7]{x}$ e $1835008 \sqrt[7]{x}$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x + 0$

Etapa 5.2.4.13.2

Some $x$ e $0$ .

$f^{- 1} (\frac{\sqrt[7]{x} - 8}{3}) = x$

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 $f (2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 3870720 x^{3} + 6193152 x^{2} + 5505024 x + 2097152)$ substituindo o valor de $f^{- 1}$ em $f$ .

$f (2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 3870720 x^{3} + 6193152 x^{2} + 5505024 x + 2097152) = \frac{\sqrt[7]{2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 3870720 x^{3} + 6193152 x^{2} + 5505024 x + 2097152} - 8}{3}$

Etapa 5.4

Como $f^{- 1} (f (x)) = x$ e $f (f^{- 1} (x)) = x$ , então, $f^{- 1} (x) = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 3870720 x^{3} + 6193152 x^{2} + 5505024 x + 2097152$ é o inverso de $f (x) = \frac{\sqrt[7]{x} - 8}{3}$ .

$f^{- 1} (x) = 2187 x^{7} + 40824 x^{6} + 326592 x^{5} + 1451520 x^{4} + 3870720 x^{3} + 6193152 x^{2} + 5505024 x + 2097152$