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Simplify. $\newline$ $(-32)^{1/5}$ $\newline$ ______

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Evaluate integers raised to rational exponents

Full solution

Q. Simplify.

\newline

(-32)^{1/5}

\newline

______

Recognize exponent as fifth root: We need to simplify the expression $(-32)^{\frac{1}{5}}$ . $\newline$ First, we recognize that the exponent $\frac{1}{5}$ represents the fifth root.
Apply exponent rule: We can apply the exponent rule that states $(-a)^{\frac{1}{n}} = - (a)^{\frac{1}{n}}$ for any positive real number $a$ and positive integer $n$ . $\newline$ So, $(-32)^{\frac{1}{5}} = -(32)^{\frac{1}{5}}$ .
Find fifth root of $32$ : Now we need to find the fifth root of $32$ . $\newline$ We know that $2^5 = 32$ , so the fifth root of $32$ is $2$ .
Replace expression with result: Therefore, we can replace $(32)^{1/5}$ with $2$ . $\newline$ So, $(-32)^{1/5}$ = $-2$ .

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