Question

How do you simplify `(1/64)^(-2/3)`?

Answer 1

`512`

Explanation:

Before we begin, remember that `a^(x/y)` is equal to `root[y] (a^x)`
Also, remember that `a^-x=1/(a^x)`
Therefore, we know that `(1/64)^(-2/3)=1/(1/64^(2/3)` => `1/(root [3] ((1/64)^2)`

`1/(root [3] ((1/64)^2))=1/(root [3] ((1/4096))`
`=1/(1/16)=>16`