Question

Please select the best answer from the choices provided

Answer 1

The correct answer option is c.
`(1)/(9a^2)`.

Explanation:

We are given an expression
`(27a^(-3))^{-(2)/(3) }` and we are supposed to simplify it.

We can also write
`(27a^(-3))^{-(2)/(3) }` as
`((3^3)/(a^3) )^{-(2)/(3) }`.

We know the power rule (a^m)^n=a^{mn} which means that to raise a power to a power you need to multiply the exponents.

So multiplying the exponents to get:

`\frac{3^{(3.-(2)/(3))} }{a^{(3.(2)/(3))} }\\\\(3^(-2))/(a^2)\\ \\(1)/(3^2a^2) \\\\(1)/(9a^2)`

Therefore, the correct answer option is c.
`(1)/(9a^2)`.