To simplify the expression [tex]\(\left(x^2 y\right)^2\)[/tex], we need to distribute the exponent to each factor inside the parentheses. Here's a step-by-step explanation:
1. Identify the components inside the parentheses:
[tex]\[
\left(x^2 y\right)^2
\][/tex]
Here, we have two factors, [tex]\(x^2\)[/tex] and [tex]\(y\)[/tex].
2. Apply the exponent to each factor inside the parentheses separately:
It means raising each factor inside the parentheses to the power of 2.
For [tex]\(x^2\)[/tex]:
[tex]\[
\left(x^2\right)^2 = x^{2 \cdot 2} = x^4
\][/tex]
For [tex]\(y\)[/tex]:
[tex]\[
y^2 = y^{1 \cdot 2} = y^2
\][/tex]
3. Combine the results:
Now we have [tex]\(x^4\)[/tex] and [tex]\(y^2\)[/tex] from the above steps. Putting them together, we get:
[tex]\[
x^4 y^2
\][/tex]
Thus, the correct simplification of the expression [tex]\(\left(x^2 y\right)^2\)[/tex] is [tex]\(\boxed{x^4 y^2}\)[/tex].
