How do I simplify the expression, (3a ^ 2) ^ -3, and what is the result

Question

I found this expression in a math textbook and couldn't simplify it.

Answer 1

The pattern that this expression exhibits is called "power of a power."

 

(a^b)^c = a^bc    In words, the exponents multiply.

 

In this case, it becomes 3^-3•a^-6  which is (1/27)(1/a⁶) and that simplifies to

1/(27a⁶).  Note that I have taken care to place parentheses around the entire denominator.

Answer 2

(3a²)^-3 = 3^-3 * (a²)^-3 = (1/3³) * (1/a⁶) = 1/27a⁶