Question

evaluate the expression (2^2 x^2 /xy^2)^2 for x=3 and y=2

Answer 1

To evaluate the expression \((\frac{2^2 x^2}{xy^2})^2\) for \(x = 3\) and \(y = 2\), let's first simplify the expression.

1. Start with the inner expression:
\[
\frac{2^2 x^2}{xy^2}
\]

2. Substitute \(x = 3\) and \(y = 2\) into the expression:
\[
2^2 = 4
\]
\[
x^2 = 3^2 = 9
\]
\[
y^2 = 2^2 = 4
\]

3. Plugging these values into the fraction:
\[
\frac{4 \cdot 9}{3 \cdot 4} = \frac{36}{12} = 3
\]

4. Now, we have the simplified expression inside the parentheses as \(3\). We need to square this:
\[
(3)^2 = 9
\]

Therefore, the result of evaluating the expression \((\frac{2^2 x^2}{xy^2})^2\) for \(x = 3\) and \(y = 2\) is \(\boxed{9}\).