Question

How do you simplify `9 ^ (-3/2)`?

Answer 1

`1/27`

Explanation:

`9^(-3/2)`
`color(white)("XXX")=1/(9^(3/2))`

`color(white)("XXX")=1/((9^(1/2))^3)`

`color(white)("XXX")=1/(3^3)` (see note below)

`color(white)("XXX")=1/27`

Noite: In taking the square root of `9` I only extracted the primary root;
a secondary solution exists `1/((-3)^3) = -1/27`