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.