# How do you simplify (a^-1b^2)/(ab) times (a^2b^3)/b^-2?

Sep 4, 2016

${b}^{6}$

#### Explanation:

$\frac{\textcolor{red}{{a}^{-} 1} {b}^{2}}{a b} \times \frac{{a}^{2} {b}^{3}}{\textcolor{b l u e}{{b}^{-} 2}}$

Use the law of indices ${x}^{-} m = \frac{1}{x} ^ m$ to get rid of the negative indices.

=$\frac{{b}^{2}}{\textcolor{red}{a} a b} \times \frac{{a}^{2} {b}^{3} \textcolor{b l u e}{{b}^{2}}}{1} \text{ "larr"now simplify}$

=$\frac{{a}^{2} {b}^{7}}{{a}^{2} b}$

=${b}^{6}$