Álgebra Ejemplos

${(2 x^{3} + 3 y^{2})}^{7}$

Paso 1

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

$1$

$1 - 1$

$1 - 2 - 1$

$\dots$

$1 - 5 - 10 - 10 - 5 - 1$

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

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

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 ${(2 x^{3} + 3 y^{2})}^{7}$ , $n = 7$ de modo que los coeficientes de la expansión se corresponderán con la línea $8$ .

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

$1 a^{7} b^{0} + 7 a^{6} b + 21 a^{5} b^{2} + 35 a^{4} b^{3} + 35 a^{3} b^{4} + 21 a^{2} b^{5} + 7 a b^{6} + 1 a^{0} b^{7}$

Paso 3

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

$1 {(2 x^{3})}^{7} {(3 y^{2})}^{0} + 7 {(2 x^{3})}^{6} {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4

Simplifica cada término.

Toca para ver más pasos...

Paso 4.1

Multiplica ${(2 x^{3})}^{7}$ por $1$ .

${(2 x^{3})}^{7} {(3 y^{2})}^{0} + 7 {(2 x^{3})}^{6} {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.2

Aplica la regla del producto a $2 x^{3}$ .

$2^{7} {(x^{3})}^{7} {(3 y^{2})}^{0} + 7 {(2 x^{3})}^{6} {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.3

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

$128 {(x^{3})}^{7} {(3 y^{2})}^{0} + 7 {(2 x^{3})}^{6} {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.4

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

Toca para ver más pasos...

Paso 4.4.1

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

$128 x^{3 \cdot 7} {(3 y^{2})}^{0} + 7 {(2 x^{3})}^{6} {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.4.2

Multiplica $3$ por $7$ .

$128 x^{21} {(3 y^{2})}^{0} + 7 {(2 x^{3})}^{6} {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.5

Aplica la regla del producto a $3 y^{2}$ .

$128 x^{21} (3^{0} {(y^{2})}^{0}) + 7 {(2 x^{3})}^{6} {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.6

Reescribe con la propiedad conmutativa de la multiplicación.

$128 \cdot 3^{0} x^{21} {(y^{2})}^{0} + 7 {(2 x^{3})}^{6} {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.7

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

$128 \cdot 1 x^{21} {(y^{2})}^{0} + 7 {(2 x^{3})}^{6} {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.8

Multiplica $128$ por $1$ .

$128 x^{21} {(y^{2})}^{0} + 7 {(2 x^{3})}^{6} {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.9

Multiplica los exponentes en ${(y^{2})}^{0}$ .

Toca para ver más pasos...

Paso 4.9.1

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

$128 x^{21} y^{2 \cdot 0} + 7 {(2 x^{3})}^{6} {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.9.2

Multiplica $2$ por $0$ .

$128 x^{21} y^{0} + 7 {(2 x^{3})}^{6} {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.10

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

$128 x^{21} \cdot 1 + 7 {(2 x^{3})}^{6} {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.11

Multiplica $128$ por $1$ .

$128 x^{21} + 7 {(2 x^{3})}^{6} {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.12

Aplica la regla del producto a $2 x^{3}$ .

$128 x^{21} + 7 (2^{6} {(x^{3})}^{6}) {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.13

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

$128 x^{21} + 7 (64 {(x^{3})}^{6}) {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.14

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

Toca para ver más pasos...

Paso 4.14.1

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

$128 x^{21} + 7 (64 x^{3 \cdot 6}) {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.14.2

Multiplica $3$ por $6$ .

$128 x^{21} + 7 (64 x^{18}) {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.15

Multiplica $64$ por $7$ .

$128 x^{21} + 448 x^{18} {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.16

Simplifica.

$128 x^{21} + 448 x^{18} (3 y^{2}) + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.17

Reescribe con la propiedad conmutativa de la multiplicación.

$128 x^{21} + 448 \cdot 3 x^{18} y^{2} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.18

Multiplica $448$ por $3$ .

$128 x^{21} + 1344 x^{18} y^{2} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.19

Aplica la regla del producto a $2 x^{3}$ .

$128 x^{21} + 1344 x^{18} y^{2} + 21 (2^{5} {(x^{3})}^{5}) {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.20

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

$128 x^{21} + 1344 x^{18} y^{2} + 21 (32 {(x^{3})}^{5}) {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.21

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

Toca para ver más pasos...

Paso 4.21.1

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

$128 x^{21} + 1344 x^{18} y^{2} + 21 (32 x^{3 \cdot 5}) {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.21.2

Multiplica $3$ por $5$ .

$128 x^{21} + 1344 x^{18} y^{2} + 21 (32 x^{15}) {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.22

Multiplica $32$ por $21$ .

$128 x^{21} + 1344 x^{18} y^{2} + 672 x^{15} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.23

Aplica la regla del producto a $3 y^{2}$ .

$128 x^{21} + 1344 x^{18} y^{2} + 672 x^{15} (3^{2} {(y^{2})}^{2}) + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.24

Reescribe con la propiedad conmutativa de la multiplicación.

$128 x^{21} + 1344 x^{18} y^{2} + 672 \cdot 3^{2} x^{15} {(y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.25

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

$128 x^{21} + 1344 x^{18} y^{2} + 672 \cdot 9 x^{15} {(y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.26

Multiplica $672$ por $9$ .

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} {(y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.27

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

Toca para ver más pasos...

Paso 4.27.1

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

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{2 \cdot 2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.27.2

Multiplica $2$ por $2$ .

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.28

Aplica la regla del producto a $2 x^{3}$ .

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 35 (2^{4} {(x^{3})}^{4}) {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.29

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

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 35 (16 {(x^{3})}^{4}) {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.30

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

Toca para ver más pasos...

Paso 4.30.1

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

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 35 (16 x^{3 \cdot 4}) {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.30.2

Multiplica $3$ por $4$ .

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 35 (16 x^{12}) {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.31

Multiplica $16$ por $35$ .

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 560 x^{12} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.32

Aplica la regla del producto a $3 y^{2}$ .

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 560 x^{12} (3^{3} {(y^{2})}^{3}) + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.33

Reescribe con la propiedad conmutativa de la multiplicación.

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 560 \cdot 3^{3} x^{12} {(y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.34

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

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 560 \cdot 27 x^{12} {(y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.35

Multiplica $560$ por $27$ .

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} {(y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.36

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

Toca para ver más pasos...

Paso 4.36.1

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

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{2 \cdot 3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.36.2

Multiplica $2$ por $3$ .

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.37

Aplica la regla del producto a $2 x^{3}$ .

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 35 (2^{3} {(x^{3})}^{3}) {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.38

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

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 35 (8 {(x^{3})}^{3}) {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.39

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

Toca para ver más pasos...

Paso 4.39.1

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

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 35 (8 x^{3 \cdot 3}) {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.39.2

Multiplica $3$ por $3$ .

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 35 (8 x^{9}) {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.40

Multiplica $8$ por $35$ .

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 280 x^{9} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.41

Aplica la regla del producto a $3 y^{2}$ .

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 280 x^{9} (3^{4} {(y^{2})}^{4}) + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.42

Reescribe con la propiedad conmutativa de la multiplicación.

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 280 \cdot 3^{4} x^{9} {(y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.43

Eleva $3$ a la potencia de $4$ .

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 280 \cdot 81 x^{9} {(y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.44

Multiplica $280$ por $81$ .

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} {(y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.45

Multiplica los exponentes en ${(y^{2})}^{4}$ .

Toca para ver más pasos...

Paso 4.45.1

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

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{2 \cdot 4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.45.2

Multiplica $2$ por $4$ .

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.46

Aplica la regla del producto a $2 x^{3}$ .

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 21 (2^{2} {(x^{3})}^{2}) {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.47

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

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 21 (4 {(x^{3})}^{2}) {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.48

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

Toca para ver más pasos...

Paso 4.48.1

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

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 21 (4 x^{3 \cdot 2}) {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.48.2

Multiplica $3$ por $2$ .

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 21 (4 x^{6}) {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.49

Multiplica $4$ por $21$ .

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 84 x^{6} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.50

Aplica la regla del producto a $3 y^{2}$ .

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 84 x^{6} (3^{5} {(y^{2})}^{5}) + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.51

Reescribe con la propiedad conmutativa de la multiplicación.

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 84 \cdot 3^{5} x^{6} {(y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.52

Eleva $3$ a la potencia de $5$ .

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 84 \cdot 243 x^{6} {(y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.53

Multiplica $84$ por $243$ .

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} {(y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.54

Multiplica los exponentes en ${(y^{2})}^{5}$ .

Toca para ver más pasos...

Paso 4.54.1

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

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{2 \cdot 5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.54.2

Multiplica $2$ por $5$ .

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.55

Simplifica.

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 7 (2 x^{3}) {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.56

Multiplica $2$ por $7$ .

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 14 x^{3} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.57

Aplica la regla del producto a $3 y^{2}$ .

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 14 x^{3} (3^{6} {(y^{2})}^{6}) + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.58

Reescribe con la propiedad conmutativa de la multiplicación.

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 14 \cdot 3^{6} x^{3} {(y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.59

Eleva $3$ a la potencia de $6$ .

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 14 \cdot 729 x^{3} {(y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.60

Multiplica $14$ por $729$ .

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 10206 x^{3} {(y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.61

Multiplica los exponentes en ${(y^{2})}^{6}$ .

Toca para ver más pasos...

Paso 4.61.1

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

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 10206 x^{3} y^{2 \cdot 6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.61.2

Multiplica $2$ por $6$ .

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 10206 x^{3} y^{12} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.62

Multiplica ${(2 x^{3})}^{0}$ por $1$ .

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 10206 x^{3} y^{12} + {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.63

Aplica la regla del producto a $2 x^{3}$ .

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 10206 x^{3} y^{12} + 2^{0} {(x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.64

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

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 10206 x^{3} y^{12} + 1 {(x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.65

Multiplica ${(x^{3})}^{0}$ por $1$ .

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 10206 x^{3} y^{12} + {(x^{3})}^{0} {(3 y^{2})}^{7}$

Paso 4.66

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

Toca para ver más pasos...

Paso 4.66.1

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

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 10206 x^{3} y^{12} + x^{3 \cdot 0} {(3 y^{2})}^{7}$

Paso 4.66.2

Multiplica $3$ por $0$ .

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 10206 x^{3} y^{12} + x^{0} {(3 y^{2})}^{7}$

Paso 4.67

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

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 10206 x^{3} y^{12} + 1 {(3 y^{2})}^{7}$

Paso 4.68

Multiplica ${(3 y^{2})}^{7}$ por $1$ .

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 10206 x^{3} y^{12} + {(3 y^{2})}^{7}$

Paso 4.69

Aplica la regla del producto a $3 y^{2}$ .

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 10206 x^{3} y^{12} + 3^{7} {(y^{2})}^{7}$

Paso 4.70

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

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 10206 x^{3} y^{12} + 2187 {(y^{2})}^{7}$

Paso 4.71

Multiplica los exponentes en ${(y^{2})}^{7}$ .

Toca para ver más pasos...

Paso 4.71.1

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

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 10206 x^{3} y^{12} + 2187 y^{2 \cdot 7}$

Paso 4.71.2

Multiplica $2$ por $7$ .

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 10206 x^{3} y^{12} + 2187 y^{14}$