Let's solve the given tasks:

1. Write $(3a)^3$ without exponents:

   $(3a)^3 = (3a) \cdot (3a) \cdot (3a) = 3 \cdot 3 \cdot 3 \cdot a \cdot a \cdot a = 27a^3$.

2. Fill in the blanks:

   In $(3a)^3 = \_\_a^3$, the correct value for the blank is $27$, so the answer is:

   $(3a)^3 = 27a^3$.

Let me know if you have any questions or need further clarifications!

Relative questions:

1. How can we simplify expressions with exponents like $(3a)^n$?
2. Why do we separate the coefficient (3) and variable (a) when expanding?
3. What is the general rule for powers of products, such as $(xy)^n$?
4. How does the distributive property of exponents apply in this example?
5. How would this change if the exponent were negative or fractional?

Tip: When expanding powers, break down each term systematically to avoid