Answer
$-8$
Work Step by Step
RECALL:
$a^{\frac{m}{n}}=\sqrt[n]{a^m}$
With $a=-32$, $m=3$, and $n=5$, use the rule above to obtain:
$=\sqrt[5]{(-32)^3}$
Write $-32$ as a power of $5$ to obtain:
$=\sqrt[5]{[(-2)^5]^3}$
Use the rule $(a^m)^n=a^{mn}$ to obtain:
$=\sqrt[5]{(-2)^{5(3)}}
\\=\sqrt[5]{(-2)^{15}}$
Use the rule $\sqrt[n]{a^m} = a^{\frac{m}{n}}$ to obtain:
$=(-2)^{\frac{15}{5}}
\\=(-2)^3
\\=-8$
