Simplify (-3xy^2)^3

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

Step 1

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

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

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

Apply the product rule to $- 3 x$ .

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

Step 2

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

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

Step 3

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

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

$- 27 x^{3} y^{2 \cdot 3}$

Multiply $2$ by $3$ .

$- 27 x^{3} y^{6}$