# How do you simplify (e^3f^9)/(e^7f^3)?

Feb 22, 2017

See the entire simplification process below:

#### Explanation:

Solution 1) Use this rule for exponents:

${x}^{\textcolor{red}{a}} / {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} - \textcolor{b l u e}{b}}$

$\frac{{e}^{\textcolor{red}{3}} {f}^{\textcolor{red}{9}}}{{e}^{\textcolor{b l u e}{7}} {f}^{\textcolor{b l u e}{3}}} = {e}^{\textcolor{red}{3} - \textcolor{b l u e}{7}} {f}^{\textcolor{red}{9} - \textcolor{b l u e}{3}} = {e}^{-} 4 {f}^{6}$

Solution 2) Use these rules for exponents if you do not want negative exponents:

${x}^{\textcolor{red}{a}} / {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} - \textcolor{b l u e}{b}}$ and ${x}^{\textcolor{red}{a}} / {x}^{\textcolor{b l u e}{b}} = \frac{1}{x} ^ \left(\textcolor{b l u e}{b} - \textcolor{red}{a}\right)$

$\frac{{e}^{\textcolor{red}{3}} {f}^{\textcolor{red}{9}}}{{e}^{\textcolor{b l u e}{7}} {f}^{\textcolor{b l u e}{3}}} = {f}^{\textcolor{red}{9} - \textcolor{b l u e}{3}} / {e}^{\textcolor{b l u e}{7} - \textcolor{red}{3}} = {f}^{6} / {e}^{4}$