Question

Simplify:

`(-27a^9)^(2/3)`

Answer 1

Given expression: `(-27a^9)^(2/3)`

Stepwise calculation:

1. Recognize that the exponent `2/3` means taking the cube root (denominator 3) and then squaring (numerator 2), or vice versa.

2. Write `(-27a^9)^(2/3) = [(-27a^9)^(1/3)]^2`

3. Calculate `(-27)^(1/3)`.

Since –27 = –(3³), its cube root is (–3).

4. Calculate `(a^9)^(1/3)`

= `a^(9 xx 1/3)`

= a³

5. Combine: `(-27a^9)^(1/3)`

= (–3)(a³) 

= –3a³

6. Now square this result:

(–3a³)² = (–3)² × (a³)² = 9a⁶

`(-27a^9)^(2/3) = 9a^6`