Simplify ((-2xy^2)^3)^2

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

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

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

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

Multiply $3$ by $2$ .

${(- 2 x y^{2})}^{6}$

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

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

${(- 2 x)}^{6} {(y^{2})}^{6}$

Apply the product rule to $- 2 x$ .

${(- 2)}^{6} x^{6} {(y^{2})}^{6}$

Raise $- 2$ to the power of $6$ .

$64 x^{6} {(y^{2})}^{6}$

Multiply the exponents in ${(y^{2})}^{6}$ .

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

$64 x^{6} y^{2 \cdot 6}$

Multiply $2$ by $6$ .

$64 x^{6} y^{12}$