To simplify \((X^2y)^2\), we apply the power of a product rule. The rule states that \((ab)^n = a^n \cdot b^n\), where \(a\) and \(b\) are terms and \(n\) is the exponent.

In this case, we distribute the exponent 2 to both \(X^2\) and \(y\):

\[
(X^2y)^2 = (X^2)^2 \cdot y^2
\]

Now simplify each term:

\[
(X^2)^2 = X^{2 \cdot 2} = X^4
\]

\[
y^2 = y^2
\]

Thus, the simplified expression is:

\[
X^4y^2
\]

### Do you want more details or have any questions?

Here are 5 related questions to expand on this:

1. How do you simplify \((2X^2y^3)^3\)?
2. What is the rule for distributing exponents over products?
3. How do you simplify expressions with fractional exponents, like \((X^{1/2}y)^3\)?
4. How do exponents distribute over division, such as \(\left(\frac{X^2}{y}\right)^3\)?
5. How would you simplify \((X^3y^2)^4\)?

**Tip**: Always apply the power rule to each part of the expression individually before combining terms.

Learn how to simplify the expression (X^2y)^2 by applying the power of a product rule. This problem explores key algebraic concepts like exponent rules and is suitable for students in Grades 8-10. Includes step-by-step instructions to simplify to X^4y^2.

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