Simplify (3x^2y^4)^3*2x^2y^2

${(3 x^{2} y^{4})}^{3} \cdot 2 x^{2} y^{2}$

Step 1

Rewrite using the commutative property of multiplication.

$2 {(3 x^{2} y^{4})}^{3} x^{2} y^{2}$

Step 2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $3 x^{2} y^{4}$ .

$2 ({(3 x^{2})}^{3} {(y^{4})}^{3}) x^{2} y^{2}$

Apply the product rule to $3 x^{2}$ .

$2 (3^{3} {(x^{2})}^{3} {(y^{4})}^{3}) x^{2} y^{2}$

Step 3

Raise $3$ to the power of $3$ .

$2 (27 {(x^{2})}^{3} {(y^{4})}^{3}) x^{2} y^{2}$

Step 4

Multiply the exponents in ${(x^{2})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2 (27 x^{2 \cdot 3} {(y^{4})}^{3}) x^{2} y^{2}$

Multiply $2$ by $3$ .

$2 (27 x^{6} {(y^{4})}^{3}) x^{2} y^{2}$

Step 5

Multiply $x^{6}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$2 (27 (x^{2} x^{6}) {(y^{4})}^{3}) y^{2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 (27 x^{2 + 6} {(y^{4})}^{3}) y^{2}$

Add $2$ and $6$ .

$2 (27 x^{8} {(y^{4})}^{3}) y^{2}$

Step 6

Multiply the exponents in ${(y^{4})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2 (27 x^{8} y^{4 \cdot 3}) y^{2}$

Multiply $4$ by $3$ .

$2 (27 x^{8} y^{12}) y^{2}$

Step 7

Multiply $y^{12}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

$2 (27 x^{8} (y^{2} y^{12}))$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 (27 x^{8} y^{2 + 12})$

Add $2$ and $12$ .

$2 (27 x^{8} y^{14})$

Step 8

Multiply $27$ by $2$ .

$54 x^{8} y^{14}$