To simplify the expression \((x^3 y^4)^2\), follow these steps:

1. Apply the power rule for exponents: \((a^m b^n)^p = a^{m \cdot p} b^{n \cdot p}\).
2. Distribute the exponent \(2\) to both \(x^3\) and \(y^4\).

\[
(x^3 y^4)^2 = (x^3)^2 (y^4)^2
\]

Now apply the power of a power rule, which states that \((a^m)^p = a^{m \cdot p}\):

\[
(x^3)^2 = x^{3 \cdot 2} = x^6
\]
\[
(y^4)^2 = y^{4 \cdot 2} = y^8
\]

Thus, the simplified expression is:

\[
x^6 y^8
\]

Would you like more details or have any further questions?

Here are five related questions:
1. How do you simplify \((a^5 b^2)^3\)?
2. What is the general rule for powers of a product?
3. How would you simplify \((x^2 y^3 z)^4\)?
4. Can you explain the difference between \((x^m)^n\) and \(x^{m+n}\)?
5. How do you handle negative exponents in similar expressions?

**Tip:** When raising an expression to a power, always apply the exponent to each base inside the parentheses.

Learn how to simplify the expression (x^3 y^4)^2 using exponentiation rules. Follow a step-by-step breakdown of applying the power rule to both terms. Perfect for students in Grades 8-10.

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