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

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

Step 1

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

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

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

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

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

Step 2

Raise $- 2$ to the power of $3$ .

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

Step 3

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

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

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

Multiply $2$ by $3$ .

$- 8 x^{6} {(y^{4})}^{3}$

Step 4

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

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

$- 8 x^{6} y^{4 \cdot 3}$

Multiply $4$ by $3$ .

$- 8 x^{6} y^{12}$