# How do you evaluate and simplify (-243)^(1/5)?

Aug 19, 2017

-3

#### Explanation:

Since the root (denominator) is 5, and since 5 is odd, the "-" sign extracts from the radical.
${\left(- 243\right)}^{\frac{1}{5}}$ = $- {\left(243\right)}^{\frac{1}{5}}$
Since ${3}^{5} = 243$,
$- {\left(243\right)}^{\frac{1}{5}} = - {\left({3}^{5}\right)}^{\frac{1}{5}}$
$= - {\left(3\right)}^{\frac{5}{5}}$
$= - {\left(3\right)}^{1}$
$= - 3$