Question

Simplify:

`(27a^9)^((-1)/3) (64a^15)^(2/3)`

Answer 1

Let’s simplify the expression:

`(27a^9)^(-1/3) * (64a^15)^(2/3)`

Step 1: Apply the power rule: `(x^m)^n = x^(mn)`

`(27a^9)^(-1/3) = 27^(-1/3) * a^(9*(-1/3))`

= `3^(-3 * 1/3) * a^-3`

= `3^-1 * a^-3`

`(64a^15)^(2/3) = 64^(2/3) * a^(15 * 2/3)`

= `4^2 * a^10`

= `16a^10`

Step 2: Multiply the simplified parts:

`3^-1 * a^-3 * 16a^10`

= `1/3 * 16 * a^(-3 + 10)`

= `16/3 a^7`