Precálculo Ejemplos

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

Paso 1

Escribe $f (x) = 7 (x^{\frac{1}{5}} + 7)$ como una ecuación.

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

Paso 2

Intercambia las variables.

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

Paso 3

Resuelve $y$

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Paso 3.1

Reescribe la ecuación como $7 (y^{\frac{1}{5}} + 7) = x$ .

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

Paso 3.2

Divide cada término en $7 (y^{\frac{1}{5}} + 7) = x$ por $7$ y simplifica.

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Paso 3.2.1

Divide cada término en $7 (y^{\frac{1}{5}} + 7) = x$ por $7$ .

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

Paso 3.2.2

Simplifica el lado izquierdo.

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Paso 3.2.2.1

Cancela el factor común.

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

Paso 3.2.2.2

Divide $y^{\frac{1}{5}} + 7$ por $1$ .

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

Paso 3.3

Mueve todos los términos que no contengan $y$ al lado derecho de la ecuación.

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Paso 3.3.1

Resta $7$ de ambos lados de la ecuación.

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

Paso 3.3.2

Suma $\frac{x}{7}$ a ambos lados de la ecuación.

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

Paso 3.4

Eleva cada lado de la ecuación a la potencia de $5$ para eliminar el exponente fraccionario en el lado izquierdo.

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

Paso 3.5

Simplifica el exponente.

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Paso 3.5.1

Simplifica el lado izquierdo.

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Paso 3.5.1.1

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

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Paso 3.5.1.1.1

Multiplica los exponentes en ${(y^{\frac{1}{5}})}^{5}$ .

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Paso 3.5.1.1.1.1

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

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

Paso 3.5.1.1.1.2

Cancela el factor común de $5$ .

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Paso 3.5.1.1.1.2.1

Cancela el factor común.

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

Paso 3.5.1.1.1.2.2

Reescribe la expresión.

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

Paso 3.5.1.1.2

Simplifica.

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

Paso 3.5.2

Simplifica el lado derecho.

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Paso 3.5.2.1

Simplifica ${(- 7 + \frac{x}{7})}^{5}$ .

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Paso 3.5.2.1.1

Usa el teorema del binomio.

$y = {(- 7)}^{5} + 5 {(- 7)}^{4} \frac{x}{7} + 10 {(- 7)}^{3} {(\frac{x}{7})}^{2} + 10 {(- 7)}^{2} {(\frac{x}{7})}^{3} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

Paso 3.5.2.1.2

Simplifica cada término.

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Paso 3.5.2.1.2.1

Eleva $- 7$ a la potencia de $5$ .

$y = - 16807 + 5 {(- 7)}^{4} \frac{x}{7} + 10 {(- 7)}^{3} {(\frac{x}{7})}^{2} + 10 {(- 7)}^{2} {(\frac{x}{7})}^{3} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

Paso 3.5.2.1.2.2

Eleva $- 7$ a la potencia de $4$ .

$y = - 16807 + 5 \cdot 2401 \frac{x}{7} + 10 {(- 7)}^{3} {(\frac{x}{7})}^{2} + 10 {(- 7)}^{2} {(\frac{x}{7})}^{3} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

Paso 3.5.2.1.2.3

Multiplica $5$ por $2401$ .

$y = - 16807 + 12005 \frac{x}{7} + 10 {(- 7)}^{3} {(\frac{x}{7})}^{2} + 10 {(- 7)}^{2} {(\frac{x}{7})}^{3} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

Paso 3.5.2.1.2.4

Cancela el factor común de $7$ .

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Paso 3.5.2.1.2.4.1

Factoriza $7$ de $12005$ .

$y = - 16807 + 7 (1715) \frac{x}{7} + 10 {(- 7)}^{3} {(\frac{x}{7})}^{2} + 10 {(- 7)}^{2} {(\frac{x}{7})}^{3} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

Paso 3.5.2.1.2.4.2

Cancela el factor común.

$y = - 16807 + 7 \cdot 1715 \frac{x}{7} + 10 {(- 7)}^{3} {(\frac{x}{7})}^{2} + 10 {(- 7)}^{2} {(\frac{x}{7})}^{3} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

Paso 3.5.2.1.2.4.3

Reescribe la expresión.

$y = - 16807 + 1715 x + 10 {(- 7)}^{3} {(\frac{x}{7})}^{2} + 10 {(- 7)}^{2} {(\frac{x}{7})}^{3} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

Paso 3.5.2.1.2.5

Eleva $- 7$ a la potencia de $3$ .

$y = - 16807 + 1715 x + 10 \cdot - 343 {(\frac{x}{7})}^{2} + 10 {(- 7)}^{2} {(\frac{x}{7})}^{3} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

Paso 3.5.2.1.2.6

Multiplica $10$ por $- 343$ .

$y = - 16807 + 1715 x - 3430 {(\frac{x}{7})}^{2} + 10 {(- 7)}^{2} {(\frac{x}{7})}^{3} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

Paso 3.5.2.1.2.7

Aplica la regla del producto a $\frac{x}{7}$ .

$y = - 16807 + 1715 x - 3430 \frac{x^{2}}{7^{2}} + 10 {(- 7)}^{2} {(\frac{x}{7})}^{3} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

Paso 3.5.2.1.2.8

Eleva $7$ a la potencia de $2$ .

$y = - 16807 + 1715 x - 3430 \frac{x^{2}}{49} + 10 {(- 7)}^{2} {(\frac{x}{7})}^{3} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

Paso 3.5.2.1.2.9

Cancela el factor común de $49$ .

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Paso 3.5.2.1.2.9.1

Factoriza $49$ de $- 3430$ .

$y = - 16807 + 1715 x + 49 (- 70) \frac{x^{2}}{49} + 10 {(- 7)}^{2} {(\frac{x}{7})}^{3} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

Paso 3.5.2.1.2.9.2

Cancela el factor común.

$y = - 16807 + 1715 x + 49 \cdot - 70 \frac{x^{2}}{49} + 10 {(- 7)}^{2} {(\frac{x}{7})}^{3} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

Paso 3.5.2.1.2.9.3

Reescribe la expresión.

$y = - 16807 + 1715 x - 70 x^{2} + 10 {(- 7)}^{2} {(\frac{x}{7})}^{3} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

Paso 3.5.2.1.2.10

Eleva $- 7$ a la potencia de $2$ .

$y = - 16807 + 1715 x - 70 x^{2} + 10 \cdot 49 {(\frac{x}{7})}^{3} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

Paso 3.5.2.1.2.11

Multiplica $10$ por $49$ .

$y = - 16807 + 1715 x - 70 x^{2} + 490 {(\frac{x}{7})}^{3} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

Paso 3.5.2.1.2.12

Aplica la regla del producto a $\frac{x}{7}$ .

$y = - 16807 + 1715 x - 70 x^{2} + 490 \frac{x^{3}}{7^{3}} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

Paso 3.5.2.1.2.13

Eleva $7$ a la potencia de $3$ .

$y = - 16807 + 1715 x - 70 x^{2} + 490 \frac{x^{3}}{343} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

Paso 3.5.2.1.2.14

Cancela el factor común de $49$ .

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Paso 3.5.2.1.2.14.1

Factoriza $49$ de $490$ .

$y = - 16807 + 1715 x - 70 x^{2} + 49 (10) \frac{x^{3}}{343} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

Paso 3.5.2.1.2.14.2

Factoriza $49$ de $343$ .

$y = - 16807 + 1715 x - 70 x^{2} + 49 \cdot 10 \frac{x^{3}}{49 \cdot 7} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

Paso 3.5.2.1.2.14.3

Cancela el factor común.

$y = - 16807 + 1715 x - 70 x^{2} + 49 \cdot 10 \frac{x^{3}}{49 \cdot 7} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

Paso 3.5.2.1.2.14.4

Reescribe la expresión.

$y = - 16807 + 1715 x - 70 x^{2} + 10 \frac{x^{3}}{7} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

Paso 3.5.2.1.2.15

Combina $10$ y $\frac{x^{3}}{7}$ .

$y = - 16807 + 1715 x - 70 x^{2} + \frac{10 x^{3}}{7} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

Paso 3.5.2.1.2.16

Multiplica $5$ por $- 7$ .

$y = - 16807 + 1715 x - 70 x^{2} + \frac{10 x^{3}}{7} - 35 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

Paso 3.5.2.1.2.17

Aplica la regla del producto a $\frac{x}{7}$ .

$y = - 16807 + 1715 x - 70 x^{2} + \frac{10 x^{3}}{7} - 35 \frac{x^{4}}{7^{4}} + {(\frac{x}{7})}^{5}$

Paso 3.5.2.1.2.18

Eleva $7$ a la potencia de $4$ .

$y = - 16807 + 1715 x - 70 x^{2} + \frac{10 x^{3}}{7} - 35 \frac{x^{4}}{2401} + {(\frac{x}{7})}^{5}$

Paso 3.5.2.1.2.19

Cancela el factor común de $7$ .

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Paso 3.5.2.1.2.19.1

Factoriza $7$ de $- 35$ .

$y = - 16807 + 1715 x - 70 x^{2} + \frac{10 x^{3}}{7} + 7 (- 5) \frac{x^{4}}{2401} + {(\frac{x}{7})}^{5}$

Paso 3.5.2.1.2.19.2

Factoriza $7$ de $2401$ .

$y = - 16807 + 1715 x - 70 x^{2} + \frac{10 x^{3}}{7} + 7 \cdot - 5 \frac{x^{4}}{7 \cdot 343} + {(\frac{x}{7})}^{5}$

Paso 3.5.2.1.2.19.3

Cancela el factor común.

$y = - 16807 + 1715 x - 70 x^{2} + \frac{10 x^{3}}{7} + 7 \cdot - 5 \frac{x^{4}}{7 \cdot 343} + {(\frac{x}{7})}^{5}$

Paso 3.5.2.1.2.19.4

Reescribe la expresión.

$y = - 16807 + 1715 x - 70 x^{2} + \frac{10 x^{3}}{7} - 5 \frac{x^{4}}{343} + {(\frac{x}{7})}^{5}$

Paso 3.5.2.1.2.20

Combina $- 5$ y $\frac{x^{4}}{343}$ .

$y = - 16807 + 1715 x - 70 x^{2} + \frac{10 x^{3}}{7} + \frac{- 5 x^{4}}{343} + {(\frac{x}{7})}^{5}$

Paso 3.5.2.1.2.21

Mueve el negativo al frente de la fracción.

$y = - 16807 + 1715 x - 70 x^{2} + \frac{10 x^{3}}{7} - \frac{5 x^{4}}{343} + {(\frac{x}{7})}^{5}$

Paso 3.5.2.1.2.22

Aplica la regla del producto a $\frac{x}{7}$ .

$y = - 16807 + 1715 x - 70 x^{2} + \frac{10 x^{3}}{7} - \frac{5 x^{4}}{343} + \frac{x^{5}}{7^{5}}$

Paso 3.5.2.1.2.23

Eleva $7$ a la potencia de $5$ .

$y = - 16807 + 1715 x - 70 x^{2} + \frac{10 x^{3}}{7} - \frac{5 x^{4}}{343} + \frac{x^{5}}{16807}$

Paso 3.6

Simplifica $- 16807 + 1715 x - 70 x^{2} + \frac{10 x^{3}}{7} - \frac{5 x^{4}}{343} + \frac{x^{5}}{16807}$ .

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Paso 3.6.1

Mueve $- 16807$ .

$y = 1715 x - 70 x^{2} + \frac{10 x^{3}}{7} - \frac{5 x^{4}}{343} + \frac{x^{5}}{16807} - 16807$

Paso 3.6.2

Mueve $1715 x$ .

$y = - 70 x^{2} + \frac{10 x^{3}}{7} - \frac{5 x^{4}}{343} + \frac{x^{5}}{16807} + 1715 x - 16807$

Paso 3.6.3

Mueve $- 70 x^{2}$ .

$y = \frac{10 x^{3}}{7} - \frac{5 x^{4}}{343} + \frac{x^{5}}{16807} - 70 x^{2} + 1715 x - 16807$

Paso 3.6.4

Mueve $\frac{10 x^{3}}{7}$ .

$y = - \frac{5 x^{4}}{343} + \frac{x^{5}}{16807} + \frac{10 x^{3}}{7} - 70 x^{2} + 1715 x - 16807$

Paso 3.6.5

Reordena $- \frac{5 x^{4}}{343}$ y $\frac{x^{5}}{16807}$ .

$y = \frac{x^{5}}{16807} - \frac{5 x^{4}}{343} + \frac{10 x^{3}}{7} - 70 x^{2} + 1715 x - 16807$

Paso 4

Reemplaza $y$ con $f^{- 1} (x)$ para ver la respuesta final.

$f^{- 1} (x) = \frac{x^{5}}{16807} - \frac{5 x^{4}}{343} + \frac{10 x^{3}}{7} - 70 x^{2} + 1715 x - 16807$

Paso 5

Verifica si $f^{- 1} (x) = \frac{x^{5}}{16807} - \frac{5 x^{4}}{343} + \frac{10 x^{3}}{7} - 70 x^{2} + 1715 x - 16807$ es la inversa de $f (x) = 7 (x^{\frac{1}{5}} + 7)$ .

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Paso 5.1

Para verificar la inversa, comprueba si $f^{- 1} (f (x)) = x$ y $f (f^{- 1} (x)) = x$ .

Paso 5.2

Evalúa $f^{- 1} (f (x))$ .

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Paso 5.2.1

Establece la función de resultado compuesta.

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

Paso 5.2.2

Evalúa $f^{- 1} (7 (x^{\frac{1}{5}} + 7))$ mediante la sustitución del valor de $f$ en $f^{- 1}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = \frac{{(7 (x^{\frac{1}{5}} + 7))}^{5}}{16807} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3

Simplifica cada término.

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Paso 5.2.3.1

Simplifica el numerador.

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Paso 5.2.3.1.1

Aplica la regla del producto a $7 (x^{\frac{1}{5}} + 7)$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = \frac{7^{5} {(x^{\frac{1}{5}} + 7)}^{5}}{16807} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.1.2

Eleva $7$ a la potencia de $5$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = \frac{16807 {(x^{\frac{1}{5}} + 7)}^{5}}{16807} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.2

Cancela el factor común.

Paso 5.2.3.3

Divide ${(x^{\frac{1}{5}} + 7)}^{5}$ por $1$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = {(x^{\frac{1}{5}} + 7)}^{5} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.4

Usa el teorema del binomio.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = {(x^{\frac{1}{5}})}^{5} + 5 {(x^{\frac{1}{5}})}^{4} \cdot 7 + 10 {(x^{\frac{1}{5}})}^{3} \cdot 7^{2} + 10 {(x^{\frac{1}{5}})}^{2} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.5

Simplifica cada término.

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Paso 5.2.3.5.1

Multiplica los exponentes en ${(x^{\frac{1}{5}})}^{5}$ .

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Paso 5.2.3.5.1.1

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x^{\frac{1}{5} \cdot 5} + 5 {(x^{\frac{1}{5}})}^{4} \cdot 7 + 10 {(x^{\frac{1}{5}})}^{3} \cdot 7^{2} + 10 {(x^{\frac{1}{5}})}^{2} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.5.1.2

Cancela el factor común de $5$ .

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Paso 5.2.3.5.1.2.1

Cancela el factor común.

Paso 5.2.3.5.1.2.2

Reescribe la expresión.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 5 {(x^{\frac{1}{5}})}^{4} \cdot 7 + 10 {(x^{\frac{1}{5}})}^{3} \cdot 7^{2} + 10 {(x^{\frac{1}{5}})}^{2} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.5.2

Simplifica.

Paso 5.2.3.5.3

Multiplica los exponentes en ${(x^{\frac{1}{5}})}^{4}$ .

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Paso 5.2.3.5.3.1

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 5 x^{\frac{1}{5} \cdot 4} \cdot 7 + 10 {(x^{\frac{1}{5}})}^{3} \cdot 7^{2} + 10 {(x^{\frac{1}{5}})}^{2} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.5.3.2

Combina $\frac{1}{5}$ y $4$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 5 x^{\frac{4}{5}} \cdot 7 + 10 {(x^{\frac{1}{5}})}^{3} \cdot 7^{2} + 10 {(x^{\frac{1}{5}})}^{2} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.5.4

Multiplica $7$ por $5$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 10 {(x^{\frac{1}{5}})}^{3} \cdot 7^{2} + 10 {(x^{\frac{1}{5}})}^{2} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.5.5

Multiplica los exponentes en ${(x^{\frac{1}{5}})}^{3}$ .

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Paso 5.2.3.5.5.1

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 10 x^{\frac{1}{5} \cdot 3} \cdot 7^{2} + 10 {(x^{\frac{1}{5}})}^{2} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.5.5.2

Combina $\frac{1}{5}$ y $3$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 10 x^{\frac{3}{5}} \cdot 7^{2} + 10 {(x^{\frac{1}{5}})}^{2} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.5.6

Eleva $7$ a la potencia de $2$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 10 x^{\frac{3}{5}} \cdot 49 + 10 {(x^{\frac{1}{5}})}^{2} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.5.7

Multiplica $49$ por $10$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 10 {(x^{\frac{1}{5}})}^{2} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.5.8

Multiplica los exponentes en ${(x^{\frac{1}{5}})}^{2}$ .

Toca para ver más pasos...

Paso 5.2.3.5.8.1

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 10 x^{\frac{1}{5} \cdot 2} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.5.8.2

Combina $\frac{1}{5}$ y $2$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 10 x^{\frac{2}{5}} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.5.9

Eleva $7$ a la potencia de $3$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 10 x^{\frac{2}{5}} \cdot 343 + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.5.10

Multiplica $343$ por $10$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.5.11

Eleva $7$ a la potencia de $4$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 5 x^{\frac{1}{5}} \cdot 2401 + 7^{5} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.5.12

Multiplica $2401$ por $5$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 7^{5} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.5.13

Eleva $7$ a la potencia de $5$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.6

Simplifica el numerador.

Toca para ver más pasos...

Paso 5.2.3.6.1

Aplica la regla del producto a $7 (x^{\frac{1}{5}} + 7)$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - \frac{5 \cdot (7^{4} {(x^{\frac{1}{5}} + 7)}^{4})}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.6.2

Eleva $7$ a la potencia de $4$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - \frac{5 \cdot (2401 {(x^{\frac{1}{5}} + 7)}^{4})}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.6.3

Multiplica $5$ por $2401$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - \frac{12005 {(x^{\frac{1}{5}} + 7)}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.7

Factoriza $343$ de $12005 {(x^{\frac{1}{5}} + 7)}^{4}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - \frac{343 (35 {(x^{\frac{1}{5}} + 7)}^{4})}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.8

Cancela los factores comunes.

Toca para ver más pasos...

Paso 5.2.3.8.1

Factoriza $343$ de $343$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - \frac{343 (35 {(x^{\frac{1}{5}} + 7)}^{4})}{343 (1)} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.8.2

Cancela el factor común.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - \frac{343 (35 {(x^{\frac{1}{5}} + 7)}^{4})}{343 \cdot 1} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.8.3

Reescribe la expresión.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - \frac{35 {(x^{\frac{1}{5}} + 7)}^{4}}{1} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.8.4

Divide $35 {(x^{\frac{1}{5}} + 7)}^{4}$ por $1$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 {(x^{\frac{1}{5}} + 7)}^{4}) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.9

Usa el teorema del binomio.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 ({(x^{\frac{1}{5}})}^{4} + 4 {(x^{\frac{1}{5}})}^{3} \cdot 7 + 6 {(x^{\frac{1}{5}})}^{2} \cdot 7^{2} + 4 x^{\frac{1}{5}} \cdot 7^{3} + 7^{4})) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.10

Simplifica cada término.

Toca para ver más pasos...

Paso 5.2.3.10.1

Multiplica los exponentes en ${(x^{\frac{1}{5}})}^{4}$ .

Toca para ver más pasos...

Paso 5.2.3.10.1.1

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 (x^{\frac{1}{5} \cdot 4} + 4 {(x^{\frac{1}{5}})}^{3} \cdot 7 + 6 {(x^{\frac{1}{5}})}^{2} \cdot 7^{2} + 4 x^{\frac{1}{5}} \cdot 7^{3} + 7^{4})) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.10.1.2

Combina $\frac{1}{5}$ y $4$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 (x^{\frac{4}{5}} + 4 {(x^{\frac{1}{5}})}^{3} \cdot 7 + 6 {(x^{\frac{1}{5}})}^{2} \cdot 7^{2} + 4 x^{\frac{1}{5}} \cdot 7^{3} + 7^{4})) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.10.2

Multiplica los exponentes en ${(x^{\frac{1}{5}})}^{3}$ .

Toca para ver más pasos...

Paso 5.2.3.10.2.1

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 (x^{\frac{4}{5}} + 4 x^{\frac{1}{5} \cdot 3} \cdot 7 + 6 {(x^{\frac{1}{5}})}^{2} \cdot 7^{2} + 4 x^{\frac{1}{5}} \cdot 7^{3} + 7^{4})) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.10.2.2

Combina $\frac{1}{5}$ y $3$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 (x^{\frac{4}{5}} + 4 x^{\frac{3}{5}} \cdot 7 + 6 {(x^{\frac{1}{5}})}^{2} \cdot 7^{2} + 4 x^{\frac{1}{5}} \cdot 7^{3} + 7^{4})) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.10.3

Multiplica $7$ por $4$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 (x^{\frac{4}{5}} + 28 x^{\frac{3}{5}} + 6 {(x^{\frac{1}{5}})}^{2} \cdot 7^{2} + 4 x^{\frac{1}{5}} \cdot 7^{3} + 7^{4})) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.10.4

Multiplica los exponentes en ${(x^{\frac{1}{5}})}^{2}$ .

Toca para ver más pasos...

Paso 5.2.3.10.4.1

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 (x^{\frac{4}{5}} + 28 x^{\frac{3}{5}} + 6 x^{\frac{1}{5} \cdot 2} \cdot 7^{2} + 4 x^{\frac{1}{5}} \cdot 7^{3} + 7^{4})) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.10.4.2

Combina $\frac{1}{5}$ y $2$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 (x^{\frac{4}{5}} + 28 x^{\frac{3}{5}} + 6 x^{\frac{2}{5}} \cdot 7^{2} + 4 x^{\frac{1}{5}} \cdot 7^{3} + 7^{4})) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.10.5

Eleva $7$ a la potencia de $2$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 (x^{\frac{4}{5}} + 28 x^{\frac{3}{5}} + 6 x^{\frac{2}{5}} \cdot 49 + 4 x^{\frac{1}{5}} \cdot 7^{3} + 7^{4})) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.10.6

Multiplica $49$ por $6$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 (x^{\frac{4}{5}} + 28 x^{\frac{3}{5}} + 294 x^{\frac{2}{5}} + 4 x^{\frac{1}{5}} \cdot 7^{3} + 7^{4})) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.10.7

Eleva $7$ a la potencia de $3$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 (x^{\frac{4}{5}} + 28 x^{\frac{3}{5}} + 294 x^{\frac{2}{5}} + 4 x^{\frac{1}{5}} \cdot 343 + 7^{4})) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.10.8

Multiplica $343$ por $4$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 (x^{\frac{4}{5}} + 28 x^{\frac{3}{5}} + 294 x^{\frac{2}{5}} + 1372 x^{\frac{1}{5}} + 7^{4})) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.10.9

Eleva $7$ a la potencia de $4$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 (x^{\frac{4}{5}} + 28 x^{\frac{3}{5}} + 294 x^{\frac{2}{5}} + 1372 x^{\frac{1}{5}} + 2401)) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.11

Aplica la propiedad distributiva.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 x^{\frac{4}{5}} + 35 (28 x^{\frac{3}{5}}) + 35 (294 x^{\frac{2}{5}}) + 35 (1372 x^{\frac{1}{5}}) + 35 \cdot 2401) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.12

Simplifica.

Toca para ver más pasos...

Paso 5.2.3.12.1

Multiplica $28$ por $35$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 x^{\frac{4}{5}} + 980 x^{\frac{3}{5}} + 35 (294 x^{\frac{2}{5}}) + 35 (1372 x^{\frac{1}{5}}) + 35 \cdot 2401) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.12.2

Multiplica $294$ por $35$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 x^{\frac{4}{5}} + 980 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 35 (1372 x^{\frac{1}{5}}) + 35 \cdot 2401) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.12.3

Multiplica $1372$ por $35$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 x^{\frac{4}{5}} + 980 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 48020 x^{\frac{1}{5}} + 35 \cdot 2401) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.12.4

Multiplica $35$ por $2401$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 x^{\frac{4}{5}} + 980 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 48020 x^{\frac{1}{5}} + 84035) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.13

Aplica la propiedad distributiva.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 x^{\frac{4}{5}}) - (980 x^{\frac{3}{5}}) - (10290 x^{\frac{2}{5}}) - (48020 x^{\frac{1}{5}}) - 1 \cdot 84035 + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.14

Simplifica.

Toca para ver más pasos...

Paso 5.2.3.14.1

Multiplica $35$ por $- 1$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - (980 x^{\frac{3}{5}}) - (10290 x^{\frac{2}{5}}) - (48020 x^{\frac{1}{5}}) - 1 \cdot 84035 + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.14.2

Multiplica $980$ por $- 1$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - (10290 x^{\frac{2}{5}}) - (48020 x^{\frac{1}{5}}) - 1 \cdot 84035 + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.14.3

Multiplica $10290$ por $- 1$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - (48020 x^{\frac{1}{5}}) - 1 \cdot 84035 + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.14.4

Multiplica $48020$ por $- 1$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 1 \cdot 84035 + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.14.5

Multiplica $- 1$ por $84035$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.15

Simplifica el numerador.

Toca para ver más pasos...

Paso 5.2.3.15.1

Aplica la regla del producto a $7 (x^{\frac{1}{5}} + 7)$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + \frac{10 \cdot (7^{3} {(x^{\frac{1}{5}} + 7)}^{3})}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.15.2

Eleva $7$ a la potencia de $3$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + \frac{10 \cdot (343 {(x^{\frac{1}{5}} + 7)}^{3})}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.15.3

Multiplica $10$ por $343$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + \frac{3430 {(x^{\frac{1}{5}} + 7)}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.16

Factoriza $7$ de $3430 {(x^{\frac{1}{5}} + 7)}^{3}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + \frac{7 (490 {(x^{\frac{1}{5}} + 7)}^{3})}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.17

Cancela los factores comunes.

Toca para ver más pasos...

Paso 5.2.3.17.1

Factoriza $7$ de $7$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + \frac{7 (490 {(x^{\frac{1}{5}} + 7)}^{3})}{7 (1)} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.17.2

Cancela el factor común.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + \frac{7 (490 {(x^{\frac{1}{5}} + 7)}^{3})}{7 \cdot 1} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.17.3

Reescribe la expresión.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + \frac{490 {(x^{\frac{1}{5}} + 7)}^{3}}{1} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.17.4

Divide $490 {(x^{\frac{1}{5}} + 7)}^{3}$ por $1$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.18

Usa el teorema del binomio.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 ({(x^{\frac{1}{5}})}^{3} + 3 {(x^{\frac{1}{5}})}^{2} \cdot 7 + 3 x^{\frac{1}{5}} \cdot 7^{2} + 7^{3}) - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.19

Simplifica cada término.

Toca para ver más pasos...

Paso 5.2.3.19.1

Multiplica los exponentes en ${(x^{\frac{1}{5}})}^{3}$ .

Toca para ver más pasos...

Paso 5.2.3.19.1.1

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 (x^{\frac{1}{5} \cdot 3} + 3 {(x^{\frac{1}{5}})}^{2} \cdot 7 + 3 x^{\frac{1}{5}} \cdot 7^{2} + 7^{3}) - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.19.1.2

Combina $\frac{1}{5}$ y $3$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 (x^{\frac{3}{5}} + 3 {(x^{\frac{1}{5}})}^{2} \cdot 7 + 3 x^{\frac{1}{5}} \cdot 7^{2} + 7^{3}) - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.19.2

Multiplica los exponentes en ${(x^{\frac{1}{5}})}^{2}$ .

Toca para ver más pasos...

Paso 5.2.3.19.2.1

Aplica la regla de la potencia y multiplica los exponentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 (x^{\frac{3}{5}} + 3 x^{\frac{1}{5} \cdot 2} \cdot 7 + 3 x^{\frac{1}{5}} \cdot 7^{2} + 7^{3}) - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.19.2.2

Combina $\frac{1}{5}$ y $2$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 (x^{\frac{3}{5}} + 3 x^{\frac{2}{5}} \cdot 7 + 3 x^{\frac{1}{5}} \cdot 7^{2} + 7^{3}) - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.19.3

Multiplica $7$ por $3$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 (x^{\frac{3}{5}} + 21 x^{\frac{2}{5}} + 3 x^{\frac{1}{5}} \cdot 7^{2} + 7^{3}) - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.19.4

Eleva $7$ a la potencia de $2$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 (x^{\frac{3}{5}} + 21 x^{\frac{2}{5}} + 3 x^{\frac{1}{5}} \cdot 49 + 7^{3}) - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.19.5

Multiplica $49$ por $3$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 (x^{\frac{3}{5}} + 21 x^{\frac{2}{5}} + 147 x^{\frac{1}{5}} + 7^{3}) - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.19.6

Eleva $7$ a la potencia de $3$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 (x^{\frac{3}{5}} + 21 x^{\frac{2}{5}} + 147 x^{\frac{1}{5}} + 343) - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.20

Aplica la propiedad distributiva.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 490 (21 x^{\frac{2}{5}}) + 490 (147 x^{\frac{1}{5}}) + 490 \cdot 343 - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.21

Simplifica.

Toca para ver más pasos...

Paso 5.2.3.21.1

Multiplica $21$ por $490$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 490 (147 x^{\frac{1}{5}}) + 490 \cdot 343 - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.21.2

Multiplica $147$ por $490$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 490 \cdot 343 - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.21.3

Multiplica $490$ por $343$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.22

Aplica la propiedad distributiva.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 {(7 x^{\frac{1}{5}} + 7 \cdot 7)}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.23

Multiplica $7$ por $7$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 {(7 x^{\frac{1}{5}} + 49)}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.24

Reescribe ${(7 x^{\frac{1}{5}} + 49)}^{2}$ como $(7 x^{\frac{1}{5}} + 49) (7 x^{\frac{1}{5}} + 49)$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 ((7 x^{\frac{1}{5}} + 49) (7 x^{\frac{1}{5}} + 49)) + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.25

Expande $(7 x^{\frac{1}{5}} + 49) (7 x^{\frac{1}{5}} + 49)$ con el método PEIU (primero, exterior, interior, ultimo).

Toca para ver más pasos...

Paso 5.2.3.25.1

Aplica la propiedad distributiva.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 (7 x^{\frac{1}{5}} (7 x^{\frac{1}{5}} + 49) + 49 (7 x^{\frac{1}{5}} + 49)) + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.25.2

Aplica la propiedad distributiva.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 (7 x^{\frac{1}{5}} (7 x^{\frac{1}{5}}) + 7 x^{\frac{1}{5}} \cdot 49 + 49 (7 x^{\frac{1}{5}} + 49)) + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.25.3

Aplica la propiedad distributiva.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 (7 x^{\frac{1}{5}} (7 x^{\frac{1}{5}}) + 7 x^{\frac{1}{5}} \cdot 49 + 49 (7 x^{\frac{1}{5}}) + 49 \cdot 49) + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.26

Simplifica y combina los términos similares.

Toca para ver más pasos...

Paso 5.2.3.26.1

Simplifica cada término.

Toca para ver más pasos...

Paso 5.2.3.26.1.1

Reescribe con la propiedad conmutativa de la multiplicación.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 (7 \cdot (7 x^{\frac{1}{5}} x^{\frac{1}{5}}) + 7 x^{\frac{1}{5}} \cdot 49 + 49 (7 x^{\frac{1}{5}}) + 49 \cdot 49) + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.26.1.2

Multiplica $x^{\frac{1}{5}}$ por $x^{\frac{1}{5}}$ sumando los exponentes.

Toca para ver más pasos...

Paso 5.2.3.26.1.2.1

Mueve $x^{\frac{1}{5}}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 (7 \cdot (7 (x^{\frac{1}{5}} x^{\frac{1}{5}})) + 7 x^{\frac{1}{5}} \cdot 49 + 49 (7 x^{\frac{1}{5}}) + 49 \cdot 49) + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.26.1.2.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 (7 \cdot (7 x^{\frac{1}{5} + \frac{1}{5}}) + 7 x^{\frac{1}{5}} \cdot 49 + 49 (7 x^{\frac{1}{5}}) + 49 \cdot 49) + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.26.1.2.3

Combina los numeradores sobre el denominador común.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 (7 \cdot (7 x^{\frac{1 + 1}{5}}) + 7 x^{\frac{1}{5}} \cdot 49 + 49 (7 x^{\frac{1}{5}}) + 49 \cdot 49) + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.26.1.2.4

Suma $1$ y $1$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 (7 \cdot (7 x^{\frac{2}{5}}) + 7 x^{\frac{1}{5}} \cdot 49 + 49 (7 x^{\frac{1}{5}}) + 49 \cdot 49) + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.26.1.3

Multiplica $7$ por $7$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 (49 x^{\frac{2}{5}} + 7 x^{\frac{1}{5}} \cdot 49 + 49 (7 x^{\frac{1}{5}}) + 49 \cdot 49) + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.26.1.4

Multiplica $49$ por $7$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 (49 x^{\frac{2}{5}} + 343 x^{\frac{1}{5}} + 49 (7 x^{\frac{1}{5}}) + 49 \cdot 49) + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.26.1.5

Multiplica $7$ por $49$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 (49 x^{\frac{2}{5}} + 343 x^{\frac{1}{5}} + 343 x^{\frac{1}{5}} + 49 \cdot 49) + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.26.1.6

Multiplica $49$ por $49$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 (49 x^{\frac{2}{5}} + 343 x^{\frac{1}{5}} + 343 x^{\frac{1}{5}} + 2401) + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.26.2

Suma $343 x^{\frac{1}{5}}$ y $343 x^{\frac{1}{5}}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 (49 x^{\frac{2}{5}} + 686 x^{\frac{1}{5}} + 2401) + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.27

Aplica la propiedad distributiva.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 (49 x^{\frac{2}{5}}) - 70 (686 x^{\frac{1}{5}}) - 70 \cdot 2401 + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.28

Simplifica.

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Paso 5.2.3.28.1

Multiplica $49$ por $- 70$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 70 (686 x^{\frac{1}{5}}) - 70 \cdot 2401 + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.28.2

Multiplica $686$ por $- 70$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 70 \cdot 2401 + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.28.3

Multiplica $- 70$ por $2401$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 168070 + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

Paso 5.2.3.29

Aplica la propiedad distributiva.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 168070 + 1715 (7 x^{\frac{1}{5}} + 7 \cdot 7) - 16807$

Paso 5.2.3.30

Multiplica $7$ por $7$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 168070 + 1715 (7 x^{\frac{1}{5}} + 49) - 16807$

Paso 5.2.3.31

Aplica la propiedad distributiva.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 168070 + 1715 (7 x^{\frac{1}{5}}) + 1715 \cdot 49 - 16807$

Paso 5.2.3.32

Multiplica $7$ por $1715$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 168070 + 12005 x^{\frac{1}{5}} + 1715 \cdot 49 - 16807$

Paso 5.2.3.33

Multiplica $1715$ por $49$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 168070 + 12005 x^{\frac{1}{5}} + 84035 - 16807$

Paso 5.2.4

Simplifica mediante la adición de términos.

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Paso 5.2.4.1

Combina los términos opuestos en $x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 168070 + 12005 x^{\frac{1}{5}} + 84035 - 16807$ .

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Paso 5.2.4.1.1

Resta $35 x^{\frac{4}{5}}$ de $35 x^{\frac{4}{5}}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 + 0 - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 168070 + 12005 x^{\frac{1}{5}} + 84035 - 16807$

Paso 5.2.4.1.2

Suma $x + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807$ y $0$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 168070 + 12005 x^{\frac{1}{5}} + 84035 - 16807$

Paso 5.2.4.1.3

Suma $- 10290 x^{\frac{2}{5}}$ y $10290 x^{\frac{2}{5}}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 0 + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 168070 + 12005 x^{\frac{1}{5}} + 84035 - 16807$

Paso 5.2.4.1.4

Suma $x + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}}$ y $0$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 168070 + 12005 x^{\frac{1}{5}} + 84035 - 16807$

Paso 5.2.4.1.5

Resta $3430 x^{\frac{2}{5}}$ de $3430 x^{\frac{2}{5}}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 490 x^{\frac{3}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} + 168070 + 0 - 48020 x^{\frac{1}{5}} - 168070 + 12005 x^{\frac{1}{5}} + 84035 - 16807$

Paso 5.2.4.1.6

Suma $x + 490 x^{\frac{3}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} + 168070$ y $0$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 490 x^{\frac{3}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 48020 x^{\frac{1}{5}} - 168070 + 12005 x^{\frac{1}{5}} + 84035 - 16807$

Paso 5.2.4.1.7

Resta $168070$ de $168070$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 490 x^{\frac{3}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 0 + 12005 x^{\frac{1}{5}} + 84035 - 16807$

Paso 5.2.4.1.8

Suma $x + 490 x^{\frac{3}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}}$ y $0$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 490 x^{\frac{3}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}} + 84035 - 16807$

Paso 5.2.4.1.9

Suma $- 84035$ y $84035$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 490 x^{\frac{3}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}} + 0 - 16807$

Paso 5.2.4.1.10

Suma $x + 490 x^{\frac{3}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}}$ y $0$ .

Paso 5.2.4.1.11

Resta $16807$ de $16807$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 490 x^{\frac{3}{5}} + 12005 x^{\frac{1}{5}} - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}} + 0$

Paso 5.2.4.1.12

Suma $x + 490 x^{\frac{3}{5}} + 12005 x^{\frac{1}{5}} - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}}$ y $0$ .

Paso 5.2.4.2

Resta $980 x^{\frac{3}{5}}$ de $490 x^{\frac{3}{5}}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 12005 x^{\frac{1}{5}} - 490 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}}$

Paso 5.2.4.3

Combina los términos opuestos en $x + 12005 x^{\frac{1}{5}} - 490 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}}$ .

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Paso 5.2.4.3.1

Suma $- 490 x^{\frac{3}{5}}$ y $490 x^{\frac{3}{5}}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 12005 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 0 + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}}$

Paso 5.2.4.3.2

Suma $x + 12005 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}}$ y $0$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 12005 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}}$

Paso 5.2.4.4

Resta $48020 x^{\frac{1}{5}}$ de $12005 x^{\frac{1}{5}}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x - 36015 x^{\frac{1}{5}} + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}}$

Paso 5.2.4.5

Suma $- 36015 x^{\frac{1}{5}}$ y $72030 x^{\frac{1}{5}}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 36015 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}}$

Paso 5.2.4.6

Resta $48020 x^{\frac{1}{5}}$ de $36015 x^{\frac{1}{5}}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x - 12005 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}}$

Paso 5.2.4.7

Combina los términos opuestos en $x - 12005 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}}$ .

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Paso 5.2.4.7.1

Suma $- 12005 x^{\frac{1}{5}}$ y $12005 x^{\frac{1}{5}}$ .

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

Paso 5.2.4.7.2

Suma $x$ y $0$ .

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

Paso 5.3

Evalúa $f (f^{- 1} (x))$ .

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Paso 5.3.1

Establece la función de resultado compuesta.

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

Paso 5.3.2

Evalúa $f (\frac{x^{5}}{16807} - \frac{5 x^{4}}{343} + \frac{10 x^{3}}{7} - 70 x^{2} + 1715 x - 16807)$ mediante la sustitución del valor de $f^{- 1}$ en $f$ .

$f (\frac{x^{5}}{16807} - \frac{5 x^{4}}{343} + \frac{10 x^{3}}{7} - 70 x^{2} + 1715 x - 16807) = 7 ({(\frac{x^{5}}{16807} - \frac{5 x^{4}}{343} + \frac{10 x^{3}}{7} - 70 x^{2} + 1715 x - 16807)}^{\frac{1}{5}} + 7)$

Paso 5.3.3

Aplica la propiedad distributiva.

$f (\frac{x^{5}}{16807} - \frac{5 x^{4}}{343} + \frac{10 x^{3}}{7} - 70 x^{2} + 1715 x - 16807) = 7 {(\frac{x^{5}}{16807} - \frac{5 x^{4}}{343} + \frac{10 x^{3}}{7} - 70 x^{2} + 1715 x - 16807)}^{\frac{1}{5}} + 7 \cdot 7$

Paso 5.3.4

Multiplica $7$ por $7$ .

Paso 5.4

Como $f^{- 1} (f (x)) = x$ y $f (f^{- 1} (x)) = x$ , entonces $f^{- 1} (x) = \frac{x^{5}}{16807} - \frac{5 x^{4}}{343} + \frac{10 x^{3}}{7} - 70 x^{2} + 1715 x - 16807$ es la inversa de $f (x) = 7 (x^{\frac{1}{5}} + 7)$ .

$f^{- 1} (x) = \frac{x^{5}}{16807} - \frac{5 x^{4}}{343} + \frac{10 x^{3}}{7} - 70 x^{2} + 1715 x - 16807$