help with algebraic indices ?

Hi,

First time post, so forgive me if my work is a mess :) I hope you understand it.

Heres the question I have, I think I have it right, would just like someone to check it over.

$\displaystyle \frac{8*2^3*3^2}{4*4^{-2}}$

numerator

$\displaystyle {2^3*2^3*3^2}$

$\displaystyle {2^6*3^2}$

denominator

$\displaystyle {2^2*4^{-2}}$

I bring the demoninator up to the top so the negative and positives change.

$\displaystyle {2^{-2}}*{2^2*2^2}$

$\displaystyle {2^6*3^2*2^{-2}}*{2^2*2^2}$

$\displaystyle {2^8*3^2}$