The expression \((x^3)^2(y^2)^4\) can be simplified by using the **power of a power** rule, which states:

\[
(a^m)^n = a^{m \cdot n}
\]

Let's apply this rule to each part:

1. \((x^3)^2 = x^{3 \cdot 2} = x^6\)
2. \((y^2)^4 = y^{2 \cdot 4} = y^8\)

Now, multiply the two simplified expressions together:

\[
x^6 y^8
\]

Thus, \((x^3)^2(y^2)^4 = x^6 y^8\).

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you simplify \((x^5)^3(y^4)^2\)?
2. What is the rule for multiplying powers with the same base?
3. How would you simplify \((xy^2)^3\)?
4. What is the expanded form of \((x^4)^3 (y^3)^2\)?
5. Can you explain the difference between the power of a power rule and the product of powers rule?

**Tip**: When working with exponents, always remember to handle each base separately before combining terms.

This guide explains how to simplify the expression (x^3)^2(y^2)^4 using the Power of a Power Rule. Learn step-by-step how to apply exponent laws to simplify terms. Suitable for students in Grades 8-10 studying algebra and exponent rules.

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