How do you evaluate and simplify ${(- 243)}^{\frac{1}{5}}$ $(-243)^(1/5)$ ?

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How do you evaluate and simplify ${(- 243)}^{\frac{1}{5}}$ $(-243)^(1/5)$ ?

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Answer 1 · 2017-08-19T17:17:05

-3

Explanation:

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

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How do you evaluate and simplify ${(- 243)}^{\frac{1}{5}}$ $(-243)^(1/5)$ ?

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