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

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

Step 1

Simplify the numerator.

Apply the product rule to $- 2 x$ .

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

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

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

Step 2

Cancel the common factor of $x^{2}$ and $x$ .

Factor $x$ out of $4 x^{2}$ .

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

Cancel the common factors.

Factor $x$ out of $3 x y^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

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

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

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

Apply the product rule to $4 x$ .

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

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

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

Step 4

Raise $4$ to the power of $3$ .

$\frac{64 x^{3}}{3^{3} {(y^{2})}^{3}}$

Step 5

Simplify the denominator.

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

$\frac{64 x^{3}}{27 {(y^{2})}^{3}}$

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

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

$\frac{64 x^{3}}{27 y^{2 \cdot 3}}$

Multiply $2$ by $3$ .

$\frac{64 x^{3}}{27 y^{6}}$