Álgebra Exemplos

$f (x) = \frac{x^{\frac{1}{5}}}{9} + 7$

Etapa 1

Escreva $f (x) = \frac{x^{\frac{1}{5}}}{9} + 7$ como uma equação.

$y = \frac{x^{\frac{1}{5}}}{9} + 7$

Etapa 2

Alterne as variáveis.

$x = \frac{y^{\frac{1}{5}}}{9} + 7$

Etapa 3

Resolva $y$ .

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Etapa 3.1

Reescreva a equação como $\frac{y^{\frac{1}{5}}}{9} + 7 = x$ .

$\frac{y^{\frac{1}{5}}}{9} + 7 = x$

Etapa 3.2

Mova todos os termos que não contêm $y$ para o lado direito da equação.

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Etapa 3.2.1

Subtraia $7$ dos dois lados da equação.

$\frac{y^{\frac{1}{5}}}{9} - x = - 7$

Etapa 3.2.2

Some $x$ aos dois lados da equação.

$\frac{y^{\frac{1}{5}}}{9} = - 7 + x$

Etapa 3.3

Multiplique os dois lados da equação por $9$ .

$9 \frac{y^{\frac{1}{5}}}{9} = 9 (- 7 + x)$

Etapa 3.4

Simplifique os dois lados da equação.

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Etapa 3.4.1

Simplifique o lado esquerdo.

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Etapa 3.4.1.1

Cancele o fator comum de $9$ .

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Etapa 3.4.1.1.1

Cancele o fator comum.

$9 \frac{y^{\frac{1}{5}}}{9} = 9 (- 7 + x)$

Etapa 3.4.1.1.2

Reescreva a expressão.

$y^{\frac{1}{5}} = 9 (- 7 + x)$

Etapa 3.4.2

Simplifique o lado direito.

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Etapa 3.4.2.1

Simplifique $9 (- 7 + x)$ .

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Etapa 3.4.2.1.1

Aplique a propriedade distributiva.

$y^{\frac{1}{5}} = 9 \cdot - 7 + 9 x$

Etapa 3.4.2.1.2

Multiplique $9$ por $- 7$ .

$y^{\frac{1}{5}} = - 63 + 9 x$

Etapa 3.5

Eleve cada lado da equação à potência de $5$ para eliminar o expoente fracionário no lado esquerdo.

${(y^{\frac{1}{5}})}^{5} = {(- 63 + 9 x)}^{5}$

Etapa 3.6

Simplifique o expoente.

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Etapa 3.6.1

Simplifique o lado esquerdo.

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Etapa 3.6.1.1

Simplifique ${(y^{\frac{1}{5}})}^{5}$ .

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Etapa 3.6.1.1.1

Multiplique os expoentes em ${(y^{\frac{1}{5}})}^{5}$ .

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Etapa 3.6.1.1.1.1

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

$y^{\frac{1}{5} \cdot 5} = {(- 63 + 9 x)}^{5}$

Etapa 3.6.1.1.1.2

Cancele o fator comum de $5$ .

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Etapa 3.6.1.1.1.2.1

Cancele o fator comum.

$y^{\frac{1}{5} \cdot 5} = {(- 63 + 9 x)}^{5}$

Etapa 3.6.1.1.1.2.2

Reescreva a expressão.

$y^{1} = {(- 63 + 9 x)}^{5}$

Etapa 3.6.1.1.2

Simplifique.

$y = {(- 63 + 9 x)}^{5}$

Etapa 3.6.2

Simplifique o lado direito.

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Etapa 3.6.2.1

Simplifique ${(- 63 + 9 x)}^{5}$ .

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Etapa 3.6.2.1.1

Use o teorema binomial.

$y = {(- 63)}^{5} + 5 {(- 63)}^{4} (9 x) + 10 {(- 63)}^{3} {(9 x)}^{2} + 10 {(- 63)}^{2} {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

Etapa 3.6.2.1.2

Simplifique cada termo.

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Etapa 3.6.2.1.2.1

Eleve $- 63$ à potência de $5$ .

$y = - 992436543 + 5 {(- 63)}^{4} (9 x) + 10 {(- 63)}^{3} {(9 x)}^{2} + 10 {(- 63)}^{2} {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

Etapa 3.6.2.1.2.2

Eleve $- 63$ à potência de $4$ .

$y = - 992436543 + 5 \cdot 15752961 (9 x) + 10 {(- 63)}^{3} {(9 x)}^{2} + 10 {(- 63)}^{2} {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

Etapa 3.6.2.1.2.3

Multiplique $5$ por $15752961$ .

$y = - 992436543 + 78764805 (9 x) + 10 {(- 63)}^{3} {(9 x)}^{2} + 10 {(- 63)}^{2} {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

Etapa 3.6.2.1.2.4

Multiplique $9$ por $78764805$ .

$y = - 992436543 + 708883245 x + 10 {(- 63)}^{3} {(9 x)}^{2} + 10 {(- 63)}^{2} {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

Etapa 3.6.2.1.2.5

Eleve $- 63$ à potência de $3$ .

$y = - 992436543 + 708883245 x + 10 \cdot - 250047 {(9 x)}^{2} + 10 {(- 63)}^{2} {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

Etapa 3.6.2.1.2.6

Multiplique $10$ por $- 250047$ .

$y = - 992436543 + 708883245 x - 2500470 {(9 x)}^{2} + 10 {(- 63)}^{2} {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

Etapa 3.6.2.1.2.7

Aplique a regra do produto a $9 x$ .

$y = - 992436543 + 708883245 x - 2500470 (9^{2} x^{2}) + 10 {(- 63)}^{2} {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

Etapa 3.6.2.1.2.8

Eleve $9$ à potência de $2$ .

$y = - 992436543 + 708883245 x - 2500470 (81 x^{2}) + 10 {(- 63)}^{2} {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

Etapa 3.6.2.1.2.9

Multiplique $81$ por $- 2500470$ .

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 10 {(- 63)}^{2} {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

Etapa 3.6.2.1.2.10

Eleve $- 63$ à potência de $2$ .

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 10 \cdot 3969 {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

Etapa 3.6.2.1.2.11

Multiplique $10$ por $3969$ .

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 39690 {(9 x)}^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

Etapa 3.6.2.1.2.12

Aplique a regra do produto a $9 x$ .

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 39690 (9^{3} x^{3}) + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

Etapa 3.6.2.1.2.13

Eleve $9$ à potência de $3$ .

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 39690 (729 x^{3}) + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

Etapa 3.6.2.1.2.14

Multiplique $729$ por $39690$ .

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 28934010 x^{3} + 5 \cdot - 63 {(9 x)}^{4} + {(9 x)}^{5}$

Etapa 3.6.2.1.2.15

Multiplique $5$ por $- 63$ .

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 28934010 x^{3} - 315 {(9 x)}^{4} + {(9 x)}^{5}$

Etapa 3.6.2.1.2.16

Aplique a regra do produto a $9 x$ .

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 28934010 x^{3} - 315 (9^{4} x^{4}) + {(9 x)}^{5}$

Etapa 3.6.2.1.2.17

Eleve $9$ à potência de $4$ .

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 28934010 x^{3} - 315 (6561 x^{4}) + {(9 x)}^{5}$

Etapa 3.6.2.1.2.18

Multiplique $6561$ por $- 315$ .

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 28934010 x^{3} - 2066715 x^{4} + {(9 x)}^{5}$

Etapa 3.6.2.1.2.19

Aplique a regra do produto a $9 x$ .

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 28934010 x^{3} - 2066715 x^{4} + 9^{5} x^{5}$

Etapa 3.6.2.1.2.20

Eleve $9$ à potência de $5$ .

$y = - 992436543 + 708883245 x - 202538070 x^{2} + 28934010 x^{3} - 2066715 x^{4} + 59049 x^{5}$

Etapa 3.7

Simplifique $- 992436543 + 708883245 x - 202538070 x^{2} + 28934010 x^{3} - 2066715 x^{4} + 59049 x^{5}$ .

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Etapa 3.7.1

Mova $- 992436543$ .

$y = 708883245 x - 202538070 x^{2} + 28934010 x^{3} - 2066715 x^{4} + 59049 x^{5} - 992436543$

Etapa 3.7.2

Mova $708883245 x$ .

$y = - 202538070 x^{2} + 28934010 x^{3} - 2066715 x^{4} + 59049 x^{5} + 708883245 x - 992436543$

Etapa 3.7.3

Mova $- 202538070 x^{2}$ .

$y = 28934010 x^{3} - 2066715 x^{4} + 59049 x^{5} - 202538070 x^{2} + 708883245 x - 992436543$

Etapa 3.7.4

Mova $28934010 x^{3}$ .

$y = - 2066715 x^{4} + 59049 x^{5} + 28934010 x^{3} - 202538070 x^{2} + 708883245 x - 992436543$

Etapa 3.7.5

Reordene $- 2066715 x^{4}$ e $59049 x^{5}$ .

$y = 59049 x^{5} - 2066715 x^{4} + 28934010 x^{3} - 202538070 x^{2} + 708883245 x - 992436543$

Etapa 4

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

$f^{- 1} (x) = 59049 x^{5} - 2066715 x^{4} + 28934010 x^{3} - 202538070 x^{2} + 708883245 x - 992436543$

Etapa 5

Verifique se $f^{- 1} (x) = 59049 x^{5} - 2066715 x^{4} + 28934010 x^{3} - 202538070 x^{2} + 708883245 x - 992436543$ é o inverso de $f (x) = \frac{x^{\frac{1}{5}}}{9} + 7$ .

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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 $f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7)$ substituindo o valor de $f$ em $f^{- 1}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{5} - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3

Simplifique cada termo.

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Etapa 5.2.3.1

Use o teorema binomial.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 ({(\frac{x^{\frac{1}{5}}}{9})}^{5} + 5 {(\frac{x^{\frac{1}{5}}}{9})}^{4} \cdot 7 + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.2

Simplifique cada termo.

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Etapa 5.2.3.2.1

Aplique a regra do produto a $\frac{x^{\frac{1}{5}}}{9}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{{(x^{\frac{1}{5}})}^{5}}{9^{5}} + 5 {(\frac{x^{\frac{1}{5}}}{9})}^{4} \cdot 7 + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.2.2

Simplifique o numerador.

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Etapa 5.2.3.2.2.1

Multiplique os expoentes em ${(x^{\frac{1}{5}})}^{5}$ .

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Etapa 5.2.3.2.2.1.1

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x^{\frac{1}{5} \cdot 5}}{9^{5}} + 5 {(\frac{x^{\frac{1}{5}}}{9})}^{4} \cdot 7 + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.2.2.1.2

Cancele o fator comum de $5$ .

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Etapa 5.2.3.2.2.1.2.1

Cancele o fator comum.

Etapa 5.2.3.2.2.1.2.2

Reescreva a expressão.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{9^{5}} + 5 {(\frac{x^{\frac{1}{5}}}{9})}^{4} \cdot 7 + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.2.2.2

Simplifique.

Etapa 5.2.3.2.3

Eleve $9$ à potência de $5$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + 5 {(\frac{x^{\frac{1}{5}}}{9})}^{4} \cdot 7 + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.2.4

Aplique a regra do produto a $\frac{x^{\frac{1}{5}}}{9}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + 5 (\frac{{(x^{\frac{1}{5}})}^{4}}{9^{4}}) \cdot 7 + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.2.5

Multiplique os expoentes em ${(x^{\frac{1}{5}})}^{4}$ .

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Etapa 5.2.3.2.5.1

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + 5 (\frac{x^{\frac{1}{5} \cdot 4}}{9^{4}}) \cdot 7 + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.2.5.2

Combine $\frac{1}{5}$ e $4$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + 5 (\frac{x^{\frac{4}{5}}}{9^{4}}) \cdot 7 + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.2.6

Eleve $9$ à potência de $4$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + 5 (\frac{x^{\frac{4}{5}}}{6561}) \cdot 7 + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.2.7

Combine $5$ e $\frac{x^{\frac{4}{5}}}{6561}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{5 x^{\frac{4}{5}}}{6561} \cdot 7 + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.2.8

Multiplique $\frac{5 x^{\frac{4}{5}}}{6561} \cdot 7$ .

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Etapa 5.2.3.2.8.1

Combine $\frac{5 x^{\frac{4}{5}}}{6561}$ e $7$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{5 x^{\frac{4}{5}} \cdot 7}{6561} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.2.8.2

Multiplique $7$ por $5$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.2.9

Aplique a regra do produto a $\frac{x^{\frac{1}{5}}}{9}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + 10 (\frac{{(x^{\frac{1}{5}})}^{3}}{9^{3}}) \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.2.10

Multiplique os expoentes em ${(x^{\frac{1}{5}})}^{3}$ .

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Etapa 5.2.3.2.10.1

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + 10 (\frac{x^{\frac{1}{5} \cdot 3}}{9^{3}}) \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.2.10.2

Combine $\frac{1}{5}$ e $3$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + 10 (\frac{x^{\frac{3}{5}}}{9^{3}}) \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.2.11

Eleve $9$ à potência de $3$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + 10 (\frac{x^{\frac{3}{5}}}{729}) \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.2.12

Combine $10$ e $\frac{x^{\frac{3}{5}}}{729}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{10 x^{\frac{3}{5}}}{729} \cdot 7^{2} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.2.13

Eleve $7$ à potência de $2$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{10 x^{\frac{3}{5}}}{729} \cdot 49 + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.2.14

Multiplique $\frac{10 x^{\frac{3}{5}}}{729} \cdot 49$ .

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Etapa 5.2.3.2.14.1

Combine $\frac{10 x^{\frac{3}{5}}}{729}$ e $49$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{10 x^{\frac{3}{5}} \cdot 49}{729} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.2.14.2

Multiplique $49$ por $10$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + 10 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.2.15

Aplique a regra do produto a $\frac{x^{\frac{1}{5}}}{9}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + 10 (\frac{{(x^{\frac{1}{5}})}^{2}}{9^{2}}) \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.2.16

Multiplique os expoentes em ${(x^{\frac{1}{5}})}^{2}$ .

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Etapa 5.2.3.2.16.1

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + 10 (\frac{x^{\frac{1}{5} \cdot 2}}{9^{2}}) \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.2.16.2

Combine $\frac{1}{5}$ e $2$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + 10 (\frac{x^{\frac{2}{5}}}{9^{2}}) \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.2.17

Eleve $9$ à potência de $2$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + 10 (\frac{x^{\frac{2}{5}}}{81}) \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.2.18

Combine $10$ e $\frac{x^{\frac{2}{5}}}{81}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + \frac{10 x^{\frac{2}{5}}}{81} \cdot 7^{3} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.2.19

Eleve $7$ à potência de $3$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + \frac{10 x^{\frac{2}{5}}}{81} \cdot 343 + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.2.20

Multiplique $\frac{10 x^{\frac{2}{5}}}{81} \cdot 343$ .

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Etapa 5.2.3.2.20.1

Combine $\frac{10 x^{\frac{2}{5}}}{81}$ e $343$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + \frac{10 x^{\frac{2}{5}} \cdot 343}{81} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.2.20.2

Multiplique $343$ por $10$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + \frac{3430 x^{\frac{2}{5}}}{81} + 5 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.2.21

Combine $5$ e $\frac{x^{\frac{1}{5}}}{9}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + \frac{3430 x^{\frac{2}{5}}}{81} + \frac{5 x^{\frac{1}{5}}}{9} \cdot 7^{4} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.2.22

Eleve $7$ à potência de $4$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + \frac{3430 x^{\frac{2}{5}}}{81} + \frac{5 x^{\frac{1}{5}}}{9} \cdot 2401 + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.2.23

Multiplique $\frac{5 x^{\frac{1}{5}}}{9} \cdot 2401$ .

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Etapa 5.2.3.2.23.1

Combine $\frac{5 x^{\frac{1}{5}}}{9}$ e $2401$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + \frac{3430 x^{\frac{2}{5}}}{81} + \frac{5 x^{\frac{1}{5}} \cdot 2401}{9} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.2.23.2

Multiplique $2401$ por $5$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + \frac{3430 x^{\frac{2}{5}}}{81} + \frac{12005 x^{\frac{1}{5}}}{9} + 7^{5}) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.2.24

Eleve $7$ à potência de $5$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049} + \frac{35 x^{\frac{4}{5}}}{6561} + \frac{490 x^{\frac{3}{5}}}{729} + \frac{3430 x^{\frac{2}{5}}}{81} + \frac{12005 x^{\frac{1}{5}}}{9} + 16807) - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.3

Aplique a propriedade distributiva.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = 59049 (\frac{x}{59049}) + 59049 (\frac{35 x^{\frac{4}{5}}}{6561}) + 59049 (\frac{490 x^{\frac{3}{5}}}{729}) + 59049 (\frac{3430 x^{\frac{2}{5}}}{81}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.4

Simplifique.

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Etapa 5.2.3.4.1

Cancele o fator comum de $59049$ .

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Etapa 5.2.3.4.1.1

Cancele o fator comum.

Etapa 5.2.3.4.1.2

Reescreva a expressão.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 59049 (\frac{35 x^{\frac{4}{5}}}{6561}) + 59049 (\frac{490 x^{\frac{3}{5}}}{729}) + 59049 (\frac{3430 x^{\frac{2}{5}}}{81}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.4.2

Cancele o fator comum de $6561$ .

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Etapa 5.2.3.4.2.1

Fatore $6561$ de $59049$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 6561 (9) (\frac{35 x^{\frac{4}{5}}}{6561}) + 59049 (\frac{490 x^{\frac{3}{5}}}{729}) + 59049 (\frac{3430 x^{\frac{2}{5}}}{81}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.4.2.2

Cancele o fator comum.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 6561 \cdot (9 (\frac{35 x^{\frac{4}{5}}}{6561})) + 59049 (\frac{490 x^{\frac{3}{5}}}{729}) + 59049 (\frac{3430 x^{\frac{2}{5}}}{81}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.4.2.3

Reescreva a expressão.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 9 (35 x^{\frac{4}{5}}) + 59049 (\frac{490 x^{\frac{3}{5}}}{729}) + 59049 (\frac{3430 x^{\frac{2}{5}}}{81}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.4.3

Multiplique $35$ por $9$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 59049 (\frac{490 x^{\frac{3}{5}}}{729}) + 59049 (\frac{3430 x^{\frac{2}{5}}}{81}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.4.4

Cancele o fator comum de $729$ .

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Etapa 5.2.3.4.4.1

Fatore $729$ de $59049$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 729 (81) (\frac{490 x^{\frac{3}{5}}}{729}) + 59049 (\frac{3430 x^{\frac{2}{5}}}{81}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.4.4.2

Cancele o fator comum.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 729 \cdot (81 (\frac{490 x^{\frac{3}{5}}}{729})) + 59049 (\frac{3430 x^{\frac{2}{5}}}{81}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.4.4.3

Reescreva a expressão.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 81 (490 x^{\frac{3}{5}}) + 59049 (\frac{3430 x^{\frac{2}{5}}}{81}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.4.5

Multiplique $490$ por $81$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 59049 (\frac{3430 x^{\frac{2}{5}}}{81}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.4.6

Cancele o fator comum de $81$ .

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Etapa 5.2.3.4.6.1

Fatore $81$ de $59049$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 81 (729) (\frac{3430 x^{\frac{2}{5}}}{81}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.4.6.2

Cancele o fator comum.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 81 \cdot (729 (\frac{3430 x^{\frac{2}{5}}}{81})) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.4.6.3

Reescreva a expressão.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 729 (3430 x^{\frac{2}{5}}) + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.4.7

Multiplique $3430$ por $729$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 59049 (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.4.8

Cancele o fator comum de $9$ .

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Etapa 5.2.3.4.8.1

Fatore $9$ de $59049$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 9 (6561) (\frac{12005 x^{\frac{1}{5}}}{9}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.4.8.2

Cancele o fator comum.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 9 \cdot (6561 (\frac{12005 x^{\frac{1}{5}}}{9})) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.4.8.3

Reescreva a expressão.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 6561 (12005 x^{\frac{1}{5}}) + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.4.9

Multiplique $12005$ por $6561$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 59049 \cdot 16807 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.4.10

Multiplique $59049$ por $16807$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{4} + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.5

Use o teorema binomial.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 ({(\frac{x^{\frac{1}{5}}}{9})}^{4} + 4 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7 + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.6

Simplifique cada termo.

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Etapa 5.2.3.6.1

Aplique a regra do produto a $\frac{x^{\frac{1}{5}}}{9}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{{(x^{\frac{1}{5}})}^{4}}{9^{4}} + 4 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7 + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.6.2

Multiplique os expoentes em ${(x^{\frac{1}{5}})}^{4}$ .

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Etapa 5.2.3.6.2.1

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{1}{5} \cdot 4}}{9^{4}} + 4 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7 + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.6.2.2

Combine $\frac{1}{5}$ e $4$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{9^{4}} + 4 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7 + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.6.3

Eleve $9$ à potência de $4$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + 4 {(\frac{x^{\frac{1}{5}}}{9})}^{3} \cdot 7 + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.6.4

Aplique a regra do produto a $\frac{x^{\frac{1}{5}}}{9}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + 4 (\frac{{(x^{\frac{1}{5}})}^{3}}{9^{3}}) \cdot 7 + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.6.5

Multiplique os expoentes em ${(x^{\frac{1}{5}})}^{3}$ .

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Etapa 5.2.3.6.5.1

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + 4 (\frac{x^{\frac{1}{5} \cdot 3}}{9^{3}}) \cdot 7 + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.6.5.2

Combine $\frac{1}{5}$ e $3$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + 4 (\frac{x^{\frac{3}{5}}}{9^{3}}) \cdot 7 + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.6.6

Eleve $9$ à potência de $3$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + 4 (\frac{x^{\frac{3}{5}}}{729}) \cdot 7 + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.6.7

Combine $4$ e $\frac{x^{\frac{3}{5}}}{729}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{4 x^{\frac{3}{5}}}{729} \cdot 7 + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.6.8

Multiplique $\frac{4 x^{\frac{3}{5}}}{729} \cdot 7$ .

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Etapa 5.2.3.6.8.1

Combine $\frac{4 x^{\frac{3}{5}}}{729}$ e $7$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{4 x^{\frac{3}{5}} \cdot 7}{729} + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.6.8.2

Multiplique $7$ por $4$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + 6 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.6.9

Aplique a regra do produto a $\frac{x^{\frac{1}{5}}}{9}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + 6 (\frac{{(x^{\frac{1}{5}})}^{2}}{9^{2}}) \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.6.10

Multiplique os expoentes em ${(x^{\frac{1}{5}})}^{2}$ .

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Etapa 5.2.3.6.10.1

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + 6 (\frac{x^{\frac{1}{5} \cdot 2}}{9^{2}}) \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.6.10.2

Combine $\frac{1}{5}$ e $2$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + 6 (\frac{x^{\frac{2}{5}}}{9^{2}}) \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.6.11

Eleve $9$ à potência de $2$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + 6 (\frac{x^{\frac{2}{5}}}{81}) \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.6.12

Cancele o fator comum de $3$ .

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Etapa 5.2.3.6.12.1

Fatore $3$ de $6$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + 3 (2) (\frac{x^{\frac{2}{5}}}{81}) \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.6.12.2

Fatore $3$ de $81$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + 3 \cdot (2 (\frac{x^{\frac{2}{5}}}{3 \cdot 27})) \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.6.12.3

Cancele o fator comum.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + 3 \cdot (2 (\frac{x^{\frac{2}{5}}}{3 \cdot 27})) \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.6.12.4

Reescreva a expressão.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + 2 (\frac{x^{\frac{2}{5}}}{27}) \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.6.13

Combine $2$ e $\frac{x^{\frac{2}{5}}}{27}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + \frac{2 x^{\frac{2}{5}}}{27} \cdot 7^{2} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.6.14

Eleve $7$ à potência de $2$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + \frac{2 x^{\frac{2}{5}}}{27} \cdot 49 + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.6.15

Multiplique $\frac{2 x^{\frac{2}{5}}}{27} \cdot 49$ .

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Etapa 5.2.3.6.15.1

Combine $\frac{2 x^{\frac{2}{5}}}{27}$ e $49$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + \frac{2 x^{\frac{2}{5}} \cdot 49}{27} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.6.15.2

Multiplique $49$ por $2$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + \frac{98 x^{\frac{2}{5}}}{27} + 4 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.6.16

Combine $4$ e $\frac{x^{\frac{1}{5}}}{9}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + \frac{98 x^{\frac{2}{5}}}{27} + \frac{4 x^{\frac{1}{5}}}{9} \cdot 7^{3} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.6.17

Eleve $7$ à potência de $3$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + \frac{98 x^{\frac{2}{5}}}{27} + \frac{4 x^{\frac{1}{5}}}{9} \cdot 343 + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.6.18

Multiplique $\frac{4 x^{\frac{1}{5}}}{9} \cdot 343$ .

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Etapa 5.2.3.6.18.1

Combine $\frac{4 x^{\frac{1}{5}}}{9}$ e $343$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + \frac{98 x^{\frac{2}{5}}}{27} + \frac{4 x^{\frac{1}{5}} \cdot 343}{9} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.6.18.2

Multiplique $343$ por $4$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + \frac{98 x^{\frac{2}{5}}}{27} + \frac{1372 x^{\frac{1}{5}}}{9} + 7^{4}) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.6.19

Eleve $7$ à potência de $4$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 (\frac{x^{\frac{4}{5}}}{6561} + \frac{28 x^{\frac{3}{5}}}{729} + \frac{98 x^{\frac{2}{5}}}{27} + \frac{1372 x^{\frac{1}{5}}}{9} + 2401) + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.7

Aplique a propriedade distributiva.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 2066715 \frac{x^{\frac{4}{5}}}{6561} - 2066715 \frac{28 x^{\frac{3}{5}}}{729} - 2066715 \frac{98 x^{\frac{2}{5}}}{27} - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.8

Simplifique.

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Etapa 5.2.3.8.1

Cancele o fator comum de $6561$ .

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Etapa 5.2.3.8.1.1

Fatore $6561$ de $- 2066715$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 + 6561 (- 315) (\frac{x^{\frac{4}{5}}}{6561}) - 2066715 \frac{28 x^{\frac{3}{5}}}{729} - 2066715 \frac{98 x^{\frac{2}{5}}}{27} - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.8.1.2

Cancele o fator comum.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 + 6561 \cdot (- 315 \frac{x^{\frac{4}{5}}}{6561}) - 2066715 \frac{28 x^{\frac{3}{5}}}{729} - 2066715 \frac{98 x^{\frac{2}{5}}}{27} - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.8.1.3

Reescreva a expressão.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 2066715 \frac{28 x^{\frac{3}{5}}}{729} - 2066715 \frac{98 x^{\frac{2}{5}}}{27} - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.8.2

Cancele o fator comum de $729$ .

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Etapa 5.2.3.8.2.1

Fatore $729$ de $- 2066715$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} + 729 (- 2835) (\frac{28 x^{\frac{3}{5}}}{729}) - 2066715 \frac{98 x^{\frac{2}{5}}}{27} - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.8.2.2

Cancele o fator comum.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} + 729 \cdot (- 2835 \frac{28 x^{\frac{3}{5}}}{729}) - 2066715 \frac{98 x^{\frac{2}{5}}}{27} - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.8.2.3

Reescreva a expressão.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 2835 (28 x^{\frac{3}{5}}) - 2066715 \frac{98 x^{\frac{2}{5}}}{27} - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.8.3

Multiplique $28$ por $- 2835$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 2066715 \frac{98 x^{\frac{2}{5}}}{27} - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.8.4

Cancele o fator comum de $27$ .

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Etapa 5.2.3.8.4.1

Fatore $27$ de $- 2066715$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} + 27 (- 76545) (\frac{98 x^{\frac{2}{5}}}{27}) - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.8.4.2

Cancele o fator comum.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} + 27 \cdot (- 76545 \frac{98 x^{\frac{2}{5}}}{27}) - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.8.4.3

Reescreva a expressão.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 76545 (98 x^{\frac{2}{5}}) - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.8.5

Multiplique $98$ por $- 76545$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 2066715 \frac{1372 x^{\frac{1}{5}}}{9} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.8.6

Cancele o fator comum de $9$ .

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Etapa 5.2.3.8.6.1

Fatore $9$ de $- 2066715$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} + 9 (- 229635) (\frac{1372 x^{\frac{1}{5}}}{9}) - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.8.6.2

Cancele o fator comum.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} + 9 \cdot (- 229635 \frac{1372 x^{\frac{1}{5}}}{9}) - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.8.6.3

Reescreva a expressão.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 229635 (1372 x^{\frac{1}{5}}) - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.8.7

Multiplique $1372$ por $- 229635$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 2066715 \cdot 2401 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.8.8

Multiplique $- 2066715$ por $2401$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{3} - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.9

Use o teorema binomial.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 ({(\frac{x^{\frac{1}{5}}}{9})}^{3} + 3 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.10

Simplifique cada termo.

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Etapa 5.2.3.10.1

Aplique a regra do produto a $\frac{x^{\frac{1}{5}}}{9}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{{(x^{\frac{1}{5}})}^{3}}{9^{3}} + 3 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.10.2

Multiplique os expoentes em ${(x^{\frac{1}{5}})}^{3}$ .

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Etapa 5.2.3.10.2.1

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{1}{5} \cdot 3}}{9^{3}} + 3 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.10.2.2

Combine $\frac{1}{5}$ e $3$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{9^{3}} + 3 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.10.3

Eleve $9$ à potência de $3$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + 3 {(\frac{x^{\frac{1}{5}}}{9})}^{2} \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.10.4

Aplique a regra do produto a $\frac{x^{\frac{1}{5}}}{9}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + 3 (\frac{{(x^{\frac{1}{5}})}^{2}}{9^{2}}) \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.10.5

Multiplique os expoentes em ${(x^{\frac{1}{5}})}^{2}$ .

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Etapa 5.2.3.10.5.1

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + 3 (\frac{x^{\frac{1}{5} \cdot 2}}{9^{2}}) \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.10.5.2

Combine $\frac{1}{5}$ e $2$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + 3 (\frac{x^{\frac{2}{5}}}{9^{2}}) \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.10.6

Eleve $9$ à potência de $2$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + 3 (\frac{x^{\frac{2}{5}}}{81}) \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.10.7

Cancele o fator comum de $3$ .

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Etapa 5.2.3.10.7.1

Fatore $3$ de $81$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + 3 (\frac{x^{\frac{2}{5}}}{3 (27)}) \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.10.7.2

Cancele o fator comum.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + 3 (\frac{x^{\frac{2}{5}}}{3 \cdot 27}) \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.10.7.3

Reescreva a expressão.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + \frac{x^{\frac{2}{5}}}{27} \cdot 7 + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.10.8

Combine $\frac{x^{\frac{2}{5}}}{27}$ e $7$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + \frac{x^{\frac{2}{5}} \cdot 7}{27} + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.10.9

Mova $7$ para a esquerda de $x^{\frac{2}{5}}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + \frac{7 \cdot x^{\frac{2}{5}}}{27} + 3 (\frac{x^{\frac{1}{5}}}{9}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.10.10

Cancele o fator comum de $3$ .

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Etapa 5.2.3.10.10.1

Fatore $3$ de $9$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + \frac{7 x^{\frac{2}{5}}}{27} + 3 (\frac{x^{\frac{1}{5}}}{3 (3)}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.10.10.2

Cancele o fator comum.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + \frac{7 x^{\frac{2}{5}}}{27} + 3 (\frac{x^{\frac{1}{5}}}{3 \cdot 3}) \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.10.10.3

Reescreva a expressão.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + \frac{7 x^{\frac{2}{5}}}{27} + \frac{x^{\frac{1}{5}}}{3} \cdot 7^{2} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.10.11

Eleve $7$ à potência de $2$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + \frac{7 x^{\frac{2}{5}}}{27} + \frac{x^{\frac{1}{5}}}{3} \cdot 49 + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.10.12

Combine $\frac{x^{\frac{1}{5}}}{3}$ e $49$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + \frac{7 x^{\frac{2}{5}}}{27} + \frac{x^{\frac{1}{5}} \cdot 49}{3} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.10.13

Mova $49$ para a esquerda de $x^{\frac{1}{5}}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + \frac{7 x^{\frac{2}{5}}}{27} + \frac{49 \cdot x^{\frac{1}{5}}}{3} + 7^{3}) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.10.14

Eleve $7$ à potência de $3$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729} + \frac{7 x^{\frac{2}{5}}}{27} + \frac{49 x^{\frac{1}{5}}}{3} + 343) - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.11

Aplique a propriedade distributiva.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 28934010 (\frac{x^{\frac{3}{5}}}{729}) + 28934010 (\frac{7 x^{\frac{2}{5}}}{27}) + 28934010 (\frac{49 x^{\frac{1}{5}}}{3}) + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.12

Simplifique.

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Etapa 5.2.3.12.1

Cancele o fator comum de $729$ .

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Etapa 5.2.3.12.1.1

Fatore $729$ de $28934010$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 729 (39690) (\frac{x^{\frac{3}{5}}}{729}) + 28934010 (\frac{7 x^{\frac{2}{5}}}{27}) + 28934010 (\frac{49 x^{\frac{1}{5}}}{3}) + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.12.1.2

Cancele o fator comum.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 729 \cdot (39690 (\frac{x^{\frac{3}{5}}}{729})) + 28934010 (\frac{7 x^{\frac{2}{5}}}{27}) + 28934010 (\frac{49 x^{\frac{1}{5}}}{3}) + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.12.1.3

Reescreva a expressão.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 28934010 (\frac{7 x^{\frac{2}{5}}}{27}) + 28934010 (\frac{49 x^{\frac{1}{5}}}{3}) + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.12.2

Cancele o fator comum de $27$ .

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Etapa 5.2.3.12.2.1

Fatore $27$ de $28934010$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 27 (1071630) (\frac{7 x^{\frac{2}{5}}}{27}) + 28934010 (\frac{49 x^{\frac{1}{5}}}{3}) + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.12.2.2

Cancele o fator comum.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 27 \cdot (1071630 (\frac{7 x^{\frac{2}{5}}}{27})) + 28934010 (\frac{49 x^{\frac{1}{5}}}{3}) + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.12.2.3

Reescreva a expressão.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 1071630 (7 x^{\frac{2}{5}}) + 28934010 (\frac{49 x^{\frac{1}{5}}}{3}) + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.12.3

Multiplique $7$ por $1071630$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 28934010 (\frac{49 x^{\frac{1}{5}}}{3}) + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.12.4

Cancele o fator comum de $3$ .

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Etapa 5.2.3.12.4.1

Fatore $3$ de $28934010$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 3 (9644670) (\frac{49 x^{\frac{1}{5}}}{3}) + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.12.4.2

Cancele o fator comum.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 3 \cdot (9644670 (\frac{49 x^{\frac{1}{5}}}{3})) + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.12.4.3

Reescreva a expressão.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 9644670 (49 x^{\frac{1}{5}}) + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.12.5

Multiplique $49$ por $9644670$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 28934010 \cdot 343 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.12.6

Multiplique $28934010$ por $343$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 {(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2} + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.13

Reescreva ${(\frac{x^{\frac{1}{5}}}{9} + 7)}^{2}$ como $(\frac{x^{\frac{1}{5}}}{9} + 7) (\frac{x^{\frac{1}{5}}}{9} + 7)$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 ((\frac{x^{\frac{1}{5}}}{9} + 7) (\frac{x^{\frac{1}{5}}}{9} + 7)) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.14

Expanda $(\frac{x^{\frac{1}{5}}}{9} + 7) (\frac{x^{\frac{1}{5}}}{9} + 7)$ usando o método FOIL.

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Etapa 5.2.3.14.1

Aplique a propriedade distributiva.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{1}{5}}}{9} \cdot (\frac{x^{\frac{1}{5}}}{9} + 7) + 7 (\frac{x^{\frac{1}{5}}}{9} + 7)) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.14.2

Aplique a propriedade distributiva.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{1}{5}}}{9} \cdot \frac{x^{\frac{1}{5}}}{9} + \frac{x^{\frac{1}{5}}}{9} \cdot 7 + 7 (\frac{x^{\frac{1}{5}}}{9} + 7)) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.14.3

Aplique a propriedade distributiva.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{1}{5}}}{9} \cdot \frac{x^{\frac{1}{5}}}{9} + \frac{x^{\frac{1}{5}}}{9} \cdot 7 + 7 (\frac{x^{\frac{1}{5}}}{9}) + 7 \cdot 7) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.15

Simplifique e combine termos semelhantes.

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Etapa 5.2.3.15.1

Simplifique cada termo.

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Etapa 5.2.3.15.1.1

Combine.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{1}{5}} x^{\frac{1}{5}}}{9 \cdot 9} + \frac{x^{\frac{1}{5}}}{9} \cdot 7 + 7 (\frac{x^{\frac{1}{5}}}{9}) + 7 \cdot 7) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.15.1.2

Multiplique $x^{\frac{1}{5}}$ por $x^{\frac{1}{5}}$ somando os expoentes.

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Etapa 5.2.3.15.1.2.1

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

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{1}{5} + \frac{1}{5}}}{9 \cdot 9} + \frac{x^{\frac{1}{5}}}{9} \cdot 7 + 7 (\frac{x^{\frac{1}{5}}}{9}) + 7 \cdot 7) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.15.1.2.2

Combine os numeradores em relação ao denominador comum.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{1 + 1}{5}}}{9 \cdot 9} + \frac{x^{\frac{1}{5}}}{9} \cdot 7 + 7 (\frac{x^{\frac{1}{5}}}{9}) + 7 \cdot 7) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.15.1.2.3

Some $1$ e $1$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{2}{5}}}{9 \cdot 9} + \frac{x^{\frac{1}{5}}}{9} \cdot 7 + 7 (\frac{x^{\frac{1}{5}}}{9}) + 7 \cdot 7) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.15.1.3

Multiplique $9$ por $9$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{2}{5}}}{81} + \frac{x^{\frac{1}{5}}}{9} \cdot 7 + 7 (\frac{x^{\frac{1}{5}}}{9}) + 7 \cdot 7) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.15.1.4

Combine $\frac{x^{\frac{1}{5}}}{9}$ e $7$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{2}{5}}}{81} + \frac{x^{\frac{1}{5}} \cdot 7}{9} + 7 (\frac{x^{\frac{1}{5}}}{9}) + 7 \cdot 7) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.15.1.5

Mova $7$ para a esquerda de $x^{\frac{1}{5}}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{2}{5}}}{81} + \frac{7 \cdot x^{\frac{1}{5}}}{9} + 7 (\frac{x^{\frac{1}{5}}}{9}) + 7 \cdot 7) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.15.1.6

Combine $7$ e $\frac{x^{\frac{1}{5}}}{9}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{2}{5}}}{81} + \frac{7 x^{\frac{1}{5}}}{9} + \frac{7 x^{\frac{1}{5}}}{9} + 7 \cdot 7) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.15.1.7

Multiplique $7$ por $7$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{2}{5}}}{81} + \frac{7 x^{\frac{1}{5}}}{9} + \frac{7 x^{\frac{1}{5}}}{9} + 49) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.15.2

Some $\frac{7 x^{\frac{1}{5}}}{9}$ e $\frac{7 x^{\frac{1}{5}}}{9}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{2}{5}}}{81} + 2 (\frac{7 x^{\frac{1}{5}}}{9}) + 49) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.16

Multiplique $2 \frac{7 x^{\frac{1}{5}}}{9}$ .

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Etapa 5.2.3.16.1

Combine $2$ e $\frac{7 x^{\frac{1}{5}}}{9}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{2}{5}}}{81} + \frac{2 (7 x^{\frac{1}{5}})}{9} + 49) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.16.2

Multiplique $7$ por $2$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 (\frac{x^{\frac{2}{5}}}{81} + \frac{14 x^{\frac{1}{5}}}{9} + 49) + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.17

Aplique a propriedade distributiva.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 202538070 \frac{x^{\frac{2}{5}}}{81} - 202538070 \frac{14 x^{\frac{1}{5}}}{9} - 202538070 \cdot 49 + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.18

Simplifique.

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Etapa 5.2.3.18.1

Cancele o fator comum de $81$ .

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Etapa 5.2.3.18.1.1

Fatore $81$ de $- 202538070$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 + 81 (- 2500470) (\frac{x^{\frac{2}{5}}}{81}) - 202538070 \frac{14 x^{\frac{1}{5}}}{9} - 202538070 \cdot 49 + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.18.1.2

Cancele o fator comum.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 + 81 \cdot (- 2500470 \frac{x^{\frac{2}{5}}}{81}) - 202538070 \frac{14 x^{\frac{1}{5}}}{9} - 202538070 \cdot 49 + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.18.1.3

Reescreva a expressão.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 202538070 \frac{14 x^{\frac{1}{5}}}{9} - 202538070 \cdot 49 + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.18.2

Cancele o fator comum de $9$ .

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Etapa 5.2.3.18.2.1

Fatore $9$ de $- 202538070$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} + 9 (- 22504230) (\frac{14 x^{\frac{1}{5}}}{9}) - 202538070 \cdot 49 + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.18.2.2

Cancele o fator comum.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} + 9 \cdot (- 22504230 \frac{14 x^{\frac{1}{5}}}{9}) - 202538070 \cdot 49 + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.18.2.3

Reescreva a expressão.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 22504230 (14 x^{\frac{1}{5}}) - 202538070 \cdot 49 + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.18.3

Multiplique $14$ por $- 22504230$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 202538070 \cdot 49 + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.18.4

Multiplique $- 202538070$ por $49$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 9924365430 + 708883245 (\frac{x^{\frac{1}{5}}}{9} + 7) - 992436543$

Etapa 5.2.3.19

Aplique a propriedade distributiva.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 9924365430 + 708883245 (\frac{x^{\frac{1}{5}}}{9}) + 708883245 \cdot 7 - 992436543$

Etapa 5.2.3.20

Cancele o fator comum de $9$ .

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Etapa 5.2.3.20.1

Fatore $9$ de $708883245$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 9924365430 + 9 (78764805) (\frac{x^{\frac{1}{5}}}{9}) + 708883245 \cdot 7 - 992436543$

Etapa 5.2.3.20.2

Cancele o fator comum.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 9924365430 + 9 \cdot (78764805 (\frac{x^{\frac{1}{5}}}{9})) + 708883245 \cdot 7 - 992436543$

Etapa 5.2.3.20.3

Reescreva a expressão.

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 9924365430 + 78764805 x^{\frac{1}{5}} + 708883245 \cdot 7 - 992436543$

Etapa 5.2.3.21

Multiplique $708883245$ por $7$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 9924365430 + 78764805 x^{\frac{1}{5}} + 4962182715 - 992436543$

Etapa 5.2.4

Simplifique somando os termos.

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Etapa 5.2.4.1

Combine os termos opostos em $x + 315 x^{\frac{4}{5}} + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 315 x^{\frac{4}{5}} - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 9924365430 + 78764805 x^{\frac{1}{5}} + 4962182715 - 992436543$ .

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Etapa 5.2.4.1.1

Subtraia $315 x^{\frac{4}{5}}$ de $315 x^{\frac{4}{5}}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 + 0 - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 9924365430 + 78764805 x^{\frac{1}{5}} + 4962182715 - 992436543$

Etapa 5.2.4.1.2

Some $x + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543$ e $0$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 79380 x^{\frac{3}{5}} - 7501410 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 7501410 x^{\frac{2}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 9924365430 + 78764805 x^{\frac{1}{5}} + 4962182715 - 992436543$

Etapa 5.2.4.1.3

Some $- 7501410 x^{\frac{2}{5}}$ e $7501410 x^{\frac{2}{5}}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 79380 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 0 + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 9924365430 + 78764805 x^{\frac{1}{5}} + 4962182715 - 992436543$

Etapa 5.2.4.1.4

Some $x + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 79380 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}}$ e $0$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 39690 x^{\frac{3}{5}} + 2500470 x^{\frac{2}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 79380 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 2500470 x^{\frac{2}{5}} - 315059220 x^{\frac{1}{5}} - 9924365430 + 78764805 x^{\frac{1}{5}} + 4962182715 - 992436543$

Etapa 5.2.4.1.5

Subtraia $2500470 x^{\frac{2}{5}}$ de $2500470 x^{\frac{2}{5}}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 39690 x^{\frac{3}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 79380 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 + 0 - 315059220 x^{\frac{1}{5}} - 9924365430 + 78764805 x^{\frac{1}{5}} + 4962182715 - 992436543$

Etapa 5.2.4.1.6

Some $x + 39690 x^{\frac{3}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 79380 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430$ e $0$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 39690 x^{\frac{3}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 79380 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 472588830 x^{\frac{1}{5}} + 9924365430 - 315059220 x^{\frac{1}{5}} - 9924365430 + 78764805 x^{\frac{1}{5}} + 4962182715 - 992436543$

Etapa 5.2.4.1.7

Subtraia $9924365430$ de $9924365430$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 39690 x^{\frac{3}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 79380 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 472588830 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}} + 0 + 78764805 x^{\frac{1}{5}} + 4962182715 - 992436543$

Etapa 5.2.4.1.8

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 39690 x^{\frac{3}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 79380 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} - 4962182715 + 39690 x^{\frac{3}{5}} + 472588830 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}} + 78764805 x^{\frac{1}{5}} + 4962182715 - 992436543$

Etapa 5.2.4.1.9

Some $- 4962182715$ e $4962182715$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 39690 x^{\frac{3}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 79380 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} + 39690 x^{\frac{3}{5}} + 472588830 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}} + 78764805 x^{\frac{1}{5}} + 0 - 992436543$

Etapa 5.2.4.1.10

Some $x + 39690 x^{\frac{3}{5}} + 78764805 x^{\frac{1}{5}} + 992436543 - 79380 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} + 39690 x^{\frac{3}{5}} + 472588830 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}} + 78764805 x^{\frac{1}{5}}$ e $0$ .

Etapa 5.2.4.1.11

Subtraia $992436543$ de $992436543$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 39690 x^{\frac{3}{5}} + 78764805 x^{\frac{1}{5}} - 79380 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} + 39690 x^{\frac{3}{5}} + 472588830 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}} + 78764805 x^{\frac{1}{5}} + 0$

Etapa 5.2.4.1.12

Some $x + 39690 x^{\frac{3}{5}} + 78764805 x^{\frac{1}{5}} - 79380 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} + 39690 x^{\frac{3}{5}} + 472588830 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}} + 78764805 x^{\frac{1}{5}}$ e $0$ .

Etapa 5.2.4.2

Subtraia $79380 x^{\frac{3}{5}}$ de $39690 x^{\frac{3}{5}}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 78764805 x^{\frac{1}{5}} - 39690 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} + 39690 x^{\frac{3}{5}} + 472588830 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}} + 78764805 x^{\frac{1}{5}}$

Etapa 5.2.4.3

Combine os termos opostos em $x + 78764805 x^{\frac{1}{5}} - 39690 x^{\frac{3}{5}} - 315059220 x^{\frac{1}{5}} + 39690 x^{\frac{3}{5}} + 472588830 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}} + 78764805 x^{\frac{1}{5}}$ .

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Etapa 5.2.4.3.1

Some $- 39690 x^{\frac{3}{5}}$ e $39690 x^{\frac{3}{5}}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 78764805 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}} + 0 + 472588830 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}} + 78764805 x^{\frac{1}{5}}$

Etapa 5.2.4.3.2

Some $x + 78764805 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}}$ e $0$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 78764805 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}} + 472588830 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}} + 78764805 x^{\frac{1}{5}}$

Etapa 5.2.4.4

Subtraia $315059220 x^{\frac{1}{5}}$ de $78764805 x^{\frac{1}{5}}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x - 236294415 x^{\frac{1}{5}} + 472588830 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}} + 78764805 x^{\frac{1}{5}}$

Etapa 5.2.4.5

Some $- 236294415 x^{\frac{1}{5}}$ e $472588830 x^{\frac{1}{5}}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 236294415 x^{\frac{1}{5}} - 315059220 x^{\frac{1}{5}} + 78764805 x^{\frac{1}{5}}$

Etapa 5.2.4.6

Subtraia $315059220 x^{\frac{1}{5}}$ de $236294415 x^{\frac{1}{5}}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x - 78764805 x^{\frac{1}{5}} + 78764805 x^{\frac{1}{5}}$

Etapa 5.2.4.7

Combine os termos opostos em $x - 78764805 x^{\frac{1}{5}} + 78764805 x^{\frac{1}{5}}$ .

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Etapa 5.2.4.7.1

Some $- 78764805 x^{\frac{1}{5}}$ e $78764805 x^{\frac{1}{5}}$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x + 0$

Etapa 5.2.4.7.2

Some $x$ e $0$ .

$f^{- 1} (\frac{x^{\frac{1}{5}}}{9} + 7) = x$

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 $f (59049 x^{5} - 2066715 x^{4} + 28934010 x^{3} - 202538070 x^{2} + 708883245 x - 992436543)$ substituindo o valor de $f^{- 1}$ em $f$ .

$f (59049 x^{5} - 2066715 x^{4} + 28934010 x^{3} - 202538070 x^{2} + 708883245 x - 992436543) = \frac{{(59049 x^{5} - 2066715 x^{4} + 28934010 x^{3} - 202538070 x^{2} + 708883245 x - 992436543)}^{\frac{1}{5}}}{9} + 7$

Etapa 5.3.3

Para escrever $7$ como fração com um denominador comum, multiplique por $\frac{9}{9}$ .

Etapa 5.3.4

Combine $7$ e $\frac{9}{9}$ .

Etapa 5.3.5

Combine os numeradores em relação ao denominador comum.

Etapa 5.3.6

Multiplique $7$ por $9$ .

Etapa 5.4

Como $f^{- 1} (f (x)) = x$ e $f (f^{- 1} (x)) = x$ , então, $f^{- 1} (x) = 59049 x^{5} - 2066715 x^{4} + 28934010 x^{3} - 202538070 x^{2} + 708883245 x - 992436543$ é o inverso de $f (x) = \frac{x^{\frac{1}{5}}}{9} + 7$ .

$f^{- 1} (x) = 59049 x^{5} - 2066715 x^{4} + 28934010 x^{3} - 202538070 x^{2} + 708883245 x - 992436543$