Evaluate Using the Given Value ((2^2x^2)/(xy^2))^2 for x=3 and y=2

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

Step 1

Replace the variable $x$ with $3$ in the expression.

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

Step 2

Replace the variable $y$ with $2$ in the expression.

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

Step 3

Simplify the numerator.

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

${(\frac{4 \cdot 3^{2}}{3} \cdot {(2)}^{2})}^{2}$

Raise $3$ to the power of $2$ .

${(\frac{4 \cdot 9}{3} \cdot {(2)}^{2})}^{2}$

Step 4

Simplify the expression.

Multiply $4$ by $9$ .

${(\frac{36}{3} \cdot {(2)}^{2})}^{2}$

Divide $36$ by $3$ .

${(12 \cdot {(2)}^{2})}^{2}$

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

${(12 \cdot 4)}^{2}$

Multiply $12$ by $4$ .

$48^{2}$

Raise $48$ to the power of $2$ .

$2304$