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The problem asks to simplify \((3x^2)^3\).

To simplify this expression:

1. Apply the power of a power rule, which states \((a^m)^n = a^{m \cdot n}\). 
   \[
   (3x^2)^3 = 3^3 \cdot (x^2)^3
   \]

2. Calculate each part:
   - \(3^3 = 27\)
   - \((x^2)^3 = x^{2 \cdot 3} = x^6\)

Thus, the simplified expression is:
\[
27x^6
\]

The correct answer is **27x^6**.

Would you like more details or have any questions? Here are 5 related questions to explore further:

1. How would you simplify \((4x^3)^2\)?
2. What is the result of \((2x^4)^3\)?
3. How do you simplify \((5x^5)^2\)?
4. How does the power of a product rule apply to \((7xy^2)^4\)?
5. What is the expanded form of \((2x^2 + 3)^3\)?

**Tip:** When dealing with powers, always remember to distribute the exponent to both the coefficient and the variable separately!

Learn how to simplify the algebraic expression (3x^2)^3 using the power of a power rule. This detailed solution demonstrates key algebra concepts, including exponentiation and applying the power of a product rule. Suitable for Grades 8-10.

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