How do you simplify \frac { 5^ { - 5} } { 5^ { 8} }?

Jan 30, 2017

See the entire simplification process below:

Explanation:

The first rule of exponents we will use is:

${x}^{\textcolor{red}{a}} = \frac{1}{x} ^ \textcolor{red}{- a}$

${5}^{\textcolor{red}{- 5}} / {5}^{8} = \frac{1}{{5}^{\textcolor{red}{- - 5}} \cdot {5}^{8}} = \frac{1}{{5}^{5} \cdot {5}^{8}}$

The next rule of exponents to use is:

${x}^{\textcolor{red}{a}} \times {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} + \textcolor{b l u e}{b}}$

$\frac{1}{{5}^{\textcolor{red}{5}} \cdot {5}^{\textcolor{b l u e}{8}}} = \frac{1}{{5}^{\textcolor{red}{5} + \textcolor{b l u e}{8}}} = \frac{1}{5} ^ 13 = \frac{1}{1 , 220 , 703 , 125}$