Álgebra Ejemplos

${(2 x + \frac{1}{x^{3}})}^{8}$

Paso 1

El triángulo de Pascal se puede visualizar de la siguiente manera:

$1$

$1 - 1$

$1 - 2 - 1$

$\dots$

$1 - 6 - 15 - 20 - 15 - 6 - 1$

$1 - 7 - 21 - 35 - 35 - 21 - 7 - 1$

$1 - 8 - 28 - 56 - 70 - 56 - 28 - 8 - 1$

El triángulo puede usarse para calcular los coeficientes de la expansión de ${(a + b)}^{n}$ al tomar el exponente $n$ y sumar $1$ . Los coeficientes se corresponderán con la línea $n + 1$ del triángulo. Para ${(2 x + \frac{1}{x^{3}})}^{8}$ , $n = 8$ de modo que los coeficientes de la expansión se corresponderán con la línea $9$ .

Paso 2

La expansión sigue la regla ${(a + b)}^{n} = c_{0} a^{n} b^{0} + c_{1} a^{n - 1} b^{1} + c_{n - 1} a^{1} b^{n - 1} + c_{n} a^{0} b^{n}$ . Los valores de los coeficientes, desde el triángulo, son $1 - 8 - 28 - 56 - 70 - 56 - 28 - 8 - 1$ .

$1 a^{8} b^{0} + 8 a^{7} b + 28 a^{6} b^{2} + 56 a^{5} b^{3} + 70 a^{4} b^{4} + 56 a^{3} b^{5} + 28 a^{2} b^{6} + 8 a b^{7} + 1 a^{0} b^{8}$

Paso 3

Sustituye los valores reales de $a$ , $2 x$ y $b$ en la expresión $\frac{1}{x^{3}}$ .

$1 {(2 x)}^{8} {(\frac{1}{x^{3}})}^{0} + 8 {(2 x)}^{7} {(\frac{1}{x^{3}})}^{1} + 28 {(2 x)}^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4

Simplifica cada término.

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Paso 4.1

Multiplica ${(2 x)}^{8}$ por $1$ .

${(2 x)}^{8} {(\frac{1}{x^{3}})}^{0} + 8 {(2 x)}^{7} {(\frac{1}{x^{3}})}^{1} + 28 {(2 x)}^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.2

Aplica la regla del producto a $2 x$ .

$2^{8} x^{8} {(\frac{1}{x^{3}})}^{0} + 8 {(2 x)}^{7} {(\frac{1}{x^{3}})}^{1} + 28 {(2 x)}^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.3

Eleva $2$ a la potencia de $8$ .

$256 x^{8} {(\frac{1}{x^{3}})}^{0} + 8 {(2 x)}^{7} {(\frac{1}{x^{3}})}^{1} + 28 {(2 x)}^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.4

Aplica la regla del producto a $\frac{1}{x^{3}}$ .

$256 x^{8} \frac{1^{0}}{{(x^{3})}^{0}} + 8 {(2 x)}^{7} {(\frac{1}{x^{3}})}^{1} + 28 {(2 x)}^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.5

Cualquier valor elevado a $0$ es $1$ .

$256 x^{8} \frac{1}{{(x^{3})}^{0}} + 8 {(2 x)}^{7} {(\frac{1}{x^{3}})}^{1} + 28 {(2 x)}^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.6

Simplifica el denominador.

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Paso 4.6.1

Multiplica los exponentes en ${(x^{3})}^{0}$ .

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Paso 4.6.1.1

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

$256 x^{8} \frac{1}{x^{3 \cdot 0}} + 8 {(2 x)}^{7} {(\frac{1}{x^{3}})}^{1} + 28 {(2 x)}^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.6.1.2

Multiplica $3$ por $0$ .

$256 x^{8} \frac{1}{x^{0}} + 8 {(2 x)}^{7} {(\frac{1}{x^{3}})}^{1} + 28 {(2 x)}^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.6.2

Cualquier valor elevado a $0$ es $1$ .

$256 x^{8} \frac{1}{1} + 8 {(2 x)}^{7} {(\frac{1}{x^{3}})}^{1} + 28 {(2 x)}^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.7

Divide $1$ por $1$ .

$256 x^{8} \cdot 1 + 8 {(2 x)}^{7} {(\frac{1}{x^{3}})}^{1} + 28 {(2 x)}^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.8

Multiplica $256$ por $1$ .

$256 x^{8} + 8 {(2 x)}^{7} {(\frac{1}{x^{3}})}^{1} + 28 {(2 x)}^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.9

Aplica la regla del producto a $2 x$ .

$256 x^{8} + 8 (2^{7} x^{7}) {(\frac{1}{x^{3}})}^{1} + 28 {(2 x)}^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.10

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

$256 x^{8} + 8 (128 x^{7}) {(\frac{1}{x^{3}})}^{1} + 28 {(2 x)}^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.11

Multiplica $128$ por $8$ .

$256 x^{8} + 1024 x^{7} {(\frac{1}{x^{3}})}^{1} + 28 {(2 x)}^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.12

Simplifica.

$256 x^{8} + 1024 x^{7} \frac{1}{x^{3}} + 28 {(2 x)}^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.13

Cancela el factor común de $x^{3}$ .

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Paso 4.13.1

Factoriza $x^{3}$ de $1024 x^{7}$ .

$256 x^{8} + x^{3} (1024 x^{4}) \frac{1}{x^{3}} + 28 {(2 x)}^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.13.2

Cancela el factor común.

Paso 4.13.3

Reescribe la expresión.

$256 x^{8} + 1024 x^{4} + 28 {(2 x)}^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.14

Aplica la regla del producto a $2 x$ .

$256 x^{8} + 1024 x^{4} + 28 (2^{6} x^{6}) {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.15

Eleva $2$ a la potencia de $6$ .

$256 x^{8} + 1024 x^{4} + 28 (64 x^{6}) {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.16

Multiplica $64$ por $28$ .

$256 x^{8} + 1024 x^{4} + 1792 x^{6} {(\frac{1}{x^{3}})}^{2} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.17

Aplica la regla del producto a $\frac{1}{x^{3}}$ .

$256 x^{8} + 1024 x^{4} + 1792 x^{6} \frac{1^{2}}{{(x^{3})}^{2}} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.18

Uno elevado a cualquier potencia es uno.

$256 x^{8} + 1024 x^{4} + 1792 x^{6} \frac{1}{{(x^{3})}^{2}} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.19

Multiplica los exponentes en ${(x^{3})}^{2}$ .

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Paso 4.19.1

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

$256 x^{8} + 1024 x^{4} + 1792 x^{6} \frac{1}{x^{3 \cdot 2}} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.19.2

Multiplica $3$ por $2$ .

$256 x^{8} + 1024 x^{4} + 1792 x^{6} \frac{1}{x^{6}} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.20

Cancela el factor común de $x^{6}$ .

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Paso 4.20.1

Factoriza $x^{6}$ de $1792 x^{6}$ .

$256 x^{8} + 1024 x^{4} + x^{6} \cdot 1792 \frac{1}{x^{6}} + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.20.2

Cancela el factor común.

Paso 4.20.3

Reescribe la expresión.

$256 x^{8} + 1024 x^{4} + 1792 + 56 {(2 x)}^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.21

Aplica la regla del producto a $2 x$ .

$256 x^{8} + 1024 x^{4} + 1792 + 56 (2^{5} x^{5}) {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.22

Eleva $2$ a la potencia de $5$ .

$256 x^{8} + 1024 x^{4} + 1792 + 56 (32 x^{5}) {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.23

Multiplica $32$ por $56$ .

$256 x^{8} + 1024 x^{4} + 1792 + 1792 x^{5} {(\frac{1}{x^{3}})}^{3} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.24

Aplica la regla del producto a $\frac{1}{x^{3}}$ .

$256 x^{8} + 1024 x^{4} + 1792 + 1792 x^{5} \frac{1^{3}}{{(x^{3})}^{3}} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.25

Uno elevado a cualquier potencia es uno.

$256 x^{8} + 1024 x^{4} + 1792 + 1792 x^{5} \frac{1}{{(x^{3})}^{3}} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.26

Multiplica los exponentes en ${(x^{3})}^{3}$ .

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Paso 4.26.1

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

$256 x^{8} + 1024 x^{4} + 1792 + 1792 x^{5} \frac{1}{x^{3 \cdot 3}} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.26.2

Multiplica $3$ por $3$ .

$256 x^{8} + 1024 x^{4} + 1792 + 1792 x^{5} \frac{1}{x^{9}} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.27

Cancela el factor común de $x^{5}$ .

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Paso 4.27.1

Factoriza $x^{5}$ de $1792 x^{5}$ .

$256 x^{8} + 1024 x^{4} + 1792 + x^{5} \cdot 1792 \frac{1}{x^{9}} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.27.2

Factoriza $x^{5}$ de $x^{9}$ .

$256 x^{8} + 1024 x^{4} + 1792 + x^{5} \cdot 1792 \frac{1}{x^{5} x^{4}} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.27.3

Cancela el factor común.

Paso 4.27.4

Reescribe la expresión.

$256 x^{8} + 1024 x^{4} + 1792 + 1792 \frac{1}{x^{4}} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.28

Combina $1792$ y $\frac{1}{x^{4}}$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + 70 {(2 x)}^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.29

Aplica la regla del producto a $2 x$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + 70 (2^{4} x^{4}) {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.30

Eleva $2$ a la potencia de $4$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + 70 (16 x^{4}) {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.31

Multiplica $16$ por $70$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + 1120 x^{4} {(\frac{1}{x^{3}})}^{4} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.32

Aplica la regla del producto a $\frac{1}{x^{3}}$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + 1120 x^{4} \frac{1^{4}}{{(x^{3})}^{4}} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.33

Uno elevado a cualquier potencia es uno.

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + 1120 x^{4} \frac{1}{{(x^{3})}^{4}} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.34

Multiplica los exponentes en ${(x^{3})}^{4}$ .

Toca para ver más pasos...

Paso 4.34.1

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

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + 1120 x^{4} \frac{1}{x^{3 \cdot 4}} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.34.2

Multiplica $3$ por $4$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + 1120 x^{4} \frac{1}{x^{12}} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.35

Cancela el factor común de $x^{4}$ .

Toca para ver más pasos...

Paso 4.35.1

Factoriza $x^{4}$ de $1120 x^{4}$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + x^{4} \cdot 1120 \frac{1}{x^{12}} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.35.2

Factoriza $x^{4}$ de $x^{12}$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + x^{4} \cdot 1120 \frac{1}{x^{4} x^{8}} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.35.3

Cancela el factor común.

Paso 4.35.4

Reescribe la expresión.

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + 1120 \frac{1}{x^{8}} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.36

Combina $1120$ y $\frac{1}{x^{8}}$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + 56 {(2 x)}^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.37

Aplica la regla del producto a $2 x$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + 56 (2^{3} x^{3}) {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.38

Eleva $2$ a la potencia de $3$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + 56 (8 x^{3}) {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.39

Multiplica $8$ por $56$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + 448 x^{3} {(\frac{1}{x^{3}})}^{5} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.40

Aplica la regla del producto a $\frac{1}{x^{3}}$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + 448 x^{3} \frac{1^{5}}{{(x^{3})}^{5}} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.41

Uno elevado a cualquier potencia es uno.

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + 448 x^{3} \frac{1}{{(x^{3})}^{5}} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.42

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

Toca para ver más pasos...

Paso 4.42.1

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

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + 448 x^{3} \frac{1}{x^{3 \cdot 5}} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.42.2

Multiplica $3$ por $5$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + 448 x^{3} \frac{1}{x^{15}} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.43

Cancela el factor común de $x^{3}$ .

Toca para ver más pasos...

Paso 4.43.1

Factoriza $x^{3}$ de $448 x^{3}$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + x^{3} \cdot 448 \frac{1}{x^{15}} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.43.2

Factoriza $x^{3}$ de $x^{15}$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + x^{3} \cdot 448 \frac{1}{x^{3} x^{12}} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.43.3

Cancela el factor común.

Paso 4.43.4

Reescribe la expresión.

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + 448 \frac{1}{x^{12}} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.44

Combina $448$ y $\frac{1}{x^{12}}$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + 28 {(2 x)}^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.45

Aplica la regla del producto a $2 x$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + 28 (2^{2} x^{2}) {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.46

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

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + 28 (4 x^{2}) {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.47

Multiplica $4$ por $28$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + 112 x^{2} {(\frac{1}{x^{3}})}^{6} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.48

Aplica la regla del producto a $\frac{1}{x^{3}}$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + 112 x^{2} \frac{1^{6}}{{(x^{3})}^{6}} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.49

Uno elevado a cualquier potencia es uno.

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + 112 x^{2} \frac{1}{{(x^{3})}^{6}} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.50

Multiplica los exponentes en ${(x^{3})}^{6}$ .

Toca para ver más pasos...

Paso 4.50.1

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

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + 112 x^{2} \frac{1}{x^{3 \cdot 6}} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.50.2

Multiplica $3$ por $6$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + 112 x^{2} \frac{1}{x^{18}} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.51

Cancela el factor común de $x^{2}$ .

Toca para ver más pasos...

Paso 4.51.1

Factoriza $x^{2}$ de $112 x^{2}$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + x^{2} \cdot 112 \frac{1}{x^{18}} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.51.2

Factoriza $x^{2}$ de $x^{18}$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + x^{2} \cdot 112 \frac{1}{x^{2} x^{16}} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.51.3

Cancela el factor común.

Paso 4.51.4

Reescribe la expresión.

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + 112 \frac{1}{x^{16}} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.52

Combina $112$ y $\frac{1}{x^{16}}$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + 8 {(2 x)}^{1} {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.53

Simplifica.

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + 8 (2 x) {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.54

Multiplica $2$ por $8$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + 16 x {(\frac{1}{x^{3}})}^{7} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.55

Aplica la regla del producto a $\frac{1}{x^{3}}$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + 16 x \frac{1^{7}}{{(x^{3})}^{7}} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.56

Uno elevado a cualquier potencia es uno.

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + 16 x \frac{1}{{(x^{3})}^{7}} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.57

Multiplica los exponentes en ${(x^{3})}^{7}$ .

Toca para ver más pasos...

Paso 4.57.1

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

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + 16 x \frac{1}{x^{3 \cdot 7}} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.57.2

Multiplica $3$ por $7$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + 16 x \frac{1}{x^{21}} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.58

Cancela el factor común de $x$ .

Toca para ver más pasos...

Paso 4.58.1

Factoriza $x$ de $16 x$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + x \cdot 16 \frac{1}{x^{21}} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.58.2

Factoriza $x$ de $x^{21}$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + x \cdot 16 \frac{1}{x \cdot x^{20}} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.58.3

Cancela el factor común.

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + x \cdot 16 \frac{1}{x \cdot x^{20}} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.58.4

Reescribe la expresión.

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + 16 \frac{1}{x^{20}} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.59

Combina $16$ y $\frac{1}{x^{20}}$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + \frac{16}{x^{20}} + 1 {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.60

Multiplica ${(2 x)}^{0}$ por $1$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + \frac{16}{x^{20}} + {(2 x)}^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.61

Aplica la regla del producto a $2 x$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + \frac{16}{x^{20}} + 2^{0} x^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.62

Cualquier valor elevado a $0$ es $1$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + \frac{16}{x^{20}} + 1 x^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.63

Multiplica $x^{0}$ por $1$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + \frac{16}{x^{20}} + x^{0} {(\frac{1}{x^{3}})}^{8}$

Paso 4.64

Cualquier valor elevado a $0$ es $1$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + \frac{16}{x^{20}} + 1 {(\frac{1}{x^{3}})}^{8}$

Paso 4.65

Multiplica ${(\frac{1}{x^{3}})}^{8}$ por $1$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + \frac{16}{x^{20}} + {(\frac{1}{x^{3}})}^{8}$

Paso 4.66

Aplica la regla del producto a $\frac{1}{x^{3}}$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + \frac{16}{x^{20}} + \frac{1^{8}}{{(x^{3})}^{8}}$

Paso 4.67

Uno elevado a cualquier potencia es uno.

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + \frac{16}{x^{20}} + \frac{1}{{(x^{3})}^{8}}$

Paso 4.68

Multiplica los exponentes en ${(x^{3})}^{8}$ .

Toca para ver más pasos...

Paso 4.68.1

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

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + \frac{16}{x^{20}} + \frac{1}{x^{3 \cdot 8}}$

Paso 4.68.2

Multiplica $3$ por $8$ .

$256 x^{8} + 1024 x^{4} + 1792 + \frac{1792}{x^{4}} + \frac{1120}{x^{8}} + \frac{448}{x^{12}} + \frac{112}{x^{16}} + \frac{16}{x^{20}} + \frac{1}{x^{24}}$