Example with Fractions

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

Example 1

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

You use a combination of the rules you have learned and get

\begin{array}{l} \frac{a^{4} \cdot {(a^{2} \cdot b)}^{5}}{{(a \cdot b)}^{3}} & = \frac{a^{4} \cdot {(a^{2})}^{5} \cdot b^{5}}{a^{3} \cdot b^{3}} \\ = \frac{a^{4} \cdot a^{10} \cdot b^{5}}{a^{3} \cdot b^{3}} \\ = \frac{a^{14} \cdot b^{5}}{a^{3} \cdot b^{3}} \\ = a^{14 - 3} \cdot b^{5 - 3} \\ = a^{11} b^{2} \end{array}