Rewrite x^(-3/2) without negative indices.
I thought it would be x^(2/3)... why is this not correct?
Also what is the difference between indices and exponents?
so would you say that $\displaystyle \frac{-3}{2}=\frac{2}{3}$?
I think you are getting confused with what is meant by 'it becomes the inverse'. When the power is negative, it means that the 'x' (in this case) is the reciprocal.
I've explained it very badly, so here are some examples.
$\displaystyle x^{-4}=\frac{1}{x^4}$
$\displaystyle 3^{-2}=\frac{1}{3^2}$
$\displaystyle 2x^{-5}=\frac{2}{x^5}$
It's probably easier to ignore the negative part to start with, and work out what it would look like just as a fractional power. Then take the reciprocal.
Eg:
$\displaystyle x^{\displaystyle\frac{-5}{2}}$
So look at:
$\displaystyle x^{\displaystyle\frac{5}{2}}$
$\displaystyle =\sqrt{x^5}$
Therefore:
$\displaystyle x^{\displaystyle\frac{-5}{2}}$
$\displaystyle
=\frac{1}{\sqrt{x^5}}
$