The expression \((x^3)^2y\) can be simplified using the rules of exponents.

### Step-by-step simplification:

1. Use the power of a power rule: \((a^m)^n = a^{m \cdot n}\). This gives:
   \[
   (x^3)^2 = x^{3 \cdot 2} = x^6
   \]

2. Now, the expression becomes:
   \[
   x^6y
   \]

Thus, the simplified form of \((x^3)^2y\) is:
\[
x^6y
\]

Would you like more details or have any questions?

Here are some related questions you can explore:
1. How do you simplify expressions with multiple variables?
2. What are the basic rules of exponents?
3. How do you handle negative exponents in algebraic expressions?
4. What happens when exponents are fractional, such as \((x^{1/2})^2\)?
5. How can exponent rules be applied in solving polynomial equations?

**Tip:** Always apply exponent rules step by step to avoid mistakes, especially in complex expressions.

Learn how to simplify the algebraic expression (x^3)^2y by applying the power of a power rule for exponents. This problem helps students understand exponent rules, specifically how to manage powers raised to powers. Suitable for Grades 8-10 students looking to strengthen their algebra skills.

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