Simplify ((2x^2y^2)/(x^3y^3))^2

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

Cancel the common factor of $x^{2}$ and $x^{3}$ .

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $y^{2}$ and $y^{3}$ .

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

Apply the product rule to $x y$ .

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

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

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