To evaluate the expression [tex]\(\left(\frac{2^2 x^2}{x y^2}\right)^2\)[/tex] for [tex]\(x = 3\)[/tex] and [tex]\(y = 2\)[/tex], follow these steps:
1. Substitute [tex]\(x = 3\)[/tex] and [tex]\(y = 2\)[/tex] into the expression:
[tex]\[
\left(\frac{2^2 \cdot 3^2}{3 \cdot 2^2}\right)^2
\][/tex]
2. Calculate [tex]\(2^2\)[/tex]:
[tex]\[
2^2 = 4
\][/tex]
3. Calculate [tex]\(3^2\)[/tex]:
[tex]\[
3^2 = 9
\][/tex]
4. Substitute these values back into the expression:
[tex]\[
\left(\frac{4 \cdot 9}{3 \cdot 4}\right)^2
\][/tex]
5. Simplify the numerator of the fraction:
[tex]\[
4 \cdot 9 = 36
\][/tex]
6. Simplify the denominator of the fraction:
[tex]\[
3 \cdot 4 = 12
\][/tex]
7. Simplify the fraction [tex]\(\frac{36}{12}\)[/tex]:
[tex]\[
\frac{36}{12} = 3
\][/tex]
8. Now, raise the simplified result to the power of 2:
[tex]\[
3^2 = 9
\][/tex]
Therefore, the solution is [tex]\(9\)[/tex].
