Simplify (-2x^2)^3

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

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

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

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

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

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

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

$- 8 x^{2 \cdot 3}$

Multiply $2$ by $3$ .

$- 8 x^{6}$