# How do you simplify 7^(1 / 7) / 7^(-13 / 7) leaving only positive exponents?

Mar 30, 2017

${7}^{2}$

#### Explanation:

The negative exponent in the denominator can be made positive, since $\frac{1}{{7}^{- \frac{13}{7}}} = {7}^{\frac{13}{7}}$.

Hence,

$\frac{{7}^{\frac{1}{7}}}{{7}^{- \frac{13}{7}}} = {7}^{\frac{1}{7}} \cdot {7}^{\frac{13}{7}}$

$= {7}^{\frac{1 + 13}{7}}$

$= {7}^{\frac{14}{7}}$

$= {7}^{2}$