# How do you simplify ((3a)^2b^-3)/(b^-2)?

Aug 15, 2016

$\frac{9 {a}^{2}}{b}$

#### Explanation:

There are different laws of indices being used here. It does not matter in what order you apply the laws.

$\frac{\textcolor{red}{{\left(3 a\right)}^{2}} \textcolor{b l u e}{{b}^{-} 3}}{\textcolor{g r e e n}{{b}^{-} 2}}$

I like to get rid of the negative indices first.

$\frac{\textcolor{red}{{\left(3 a\right)}^{2}} \textcolor{g r e e n}{{b}^{2}}}{\textcolor{b l u e}{{b}^{3}}}$

Remove the brackets.

$\frac{\textcolor{red}{9 {a}^{2}} \textcolor{g r e e n}{{b}^{2}}}{\textcolor{b l u e}{{b}^{3}}}$

Simplify by subtracting indices of like bases. (3-2=1)

$\frac{9 {a}^{2}}{b}$