Evaluate ((2^2x^2)/(xy^2))^2

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

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

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

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

Apply the product rule to $4 x$ .

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

Raise $4$ to the power of $2$ .

$\frac{16 x^{2}}{{(y^{2})}^{2}}$

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

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

$\frac{16 x^{2}}{y^{2 \cdot 2}}$

Multiply $2$ by $2$ .

$\frac{16 x^{2}}{y^{4}}$