To solve \((3a^2)^3\), apply the power rule for exponents. Specifically, if you have \((x^m)^n\), you can simplify it as \(x^{m \cdot n}\).

Step by step:

1. Distribute the exponent to both the number and the variable:
   \[
   (3a^2)^3 = 3^3 \cdot (a^2)^3
   \]

2. Calculate \(3^3\):
   \[
   3^3 = 27
   \]

3. Use the power rule for \((a^2)^3\), which is \(a^{2 \cdot 3}\):
   \[
   (a^2)^3 = a^6
   \]

4. Combine these results:
   \[
   (3a^2)^3 = 27a^6
   \]

So the final answer is:
\[
27a^6
\]

Would you like me to explain any of the steps in more detail?

Here are 5 related questions to expand your understanding:

1. How would you simplify \((2b^3)^4\)?
2. What is the value of \((5x^2)^2 \times (x^3)^3\)?
3. Can you express \((7y^5)^2\) in simplified form?
4. How does the power rule for exponents apply to fractions like \(\left(\frac{a^2}{b^3}\right)^4\)?
5. What is the result of \((4c^2)^0\)?

**Tip:** When working with exponents, always remember that multiplying powers of the same base adds their exponents, while raising a power to a power multiplies them.

Learn how to simplify the expression (3a^2)^3 step by step by applying the power of a power rule for exponents. This problem covers algebraic concepts, focusing on exponent rules. Suitable for students in Grades 8-10.

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