# How do you write 1/169 as a negative exponent?

Mar 10, 2018

As a negative exponent, $\frac{1}{169}$ is ${13}^{-} 2$.

#### Explanation:

Rewrite $169$ as $13 \cdot 13$, then use these exponent rules:

${x}^{\textcolor{red}{m}} \cdot {x}^{\textcolor{b l u e}{n}} = {x}^{\textcolor{red}{m} + \textcolor{b l u e}{n}}$

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

Now here's the actual problem:

$\textcolor{w h i t e}{=} \frac{1}{169}$

$= \frac{1}{13 \cdot 13}$

$= \frac{1}{{13}^{\textcolor{red}{1}} \cdot {13}^{\textcolor{b l u e}{1}}}$

$= \frac{1}{{13}^{\textcolor{red}{1} + \textcolor{b l u e}{1}}}$

$= \frac{1}{{13}^{\textcolor{p u r p \le}{2}}}$

$= {13}^{\textcolor{p u r p \le}{- 2}}$

Mar 10, 2018

${13}^{-} 2$ = $\frac{1}{13} ^ 2$ = $\frac{1}{169}$