# Example with Fractions

Here is an example where you use the power rules for fractions.

Example 1

Simplify $\frac{{a}^{4}\cdot {\left({a}^{2}\cdot b\right)}^{5}}{{\left(a\cdot b\right)}^{3}}$

You use a combination of the rules you have learned and get $\begin{array}{llll}\hfill \frac{{a}^{4}\cdot {\left({a}^{2}\cdot b\right)}^{5}}{{\left(a\cdot b\right)}^{3}}& =\frac{{a}^{4}\cdot {\left({a}^{2}\right)}^{5}\cdot {b}^{5}}{{a}^{3}\cdot {b}^{3}}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =\frac{{a}^{4}\cdot {a}^{10}\cdot {b}^{5}}{{a}^{3}\cdot {b}^{3}}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =\frac{{a}^{14}\cdot {b}^{5}}{{a}^{3}\cdot {b}^{3}}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & ={a}^{14-3}\cdot {b}^{5-3}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & ={a}^{11}{b}^{2}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$