Answer
$9$
Work Step by Step
RECALL:
$a^{\frac{m}{n}}=\sqrt[n]{a^m}$
With $a=-27$, $m=2$, and $n=3$, use the rule above to obtain:
$=\sqrt[3]{(-27)^2}$
Write $-27$ as a power of $3$ to obtain:
$=\sqrt[3]{[(-3)^3]^2}$
Use the rule $(a^m)^n=a^{mn}$ to obtain:
$=\sqrt[3]{[(-3)^3]^2}
\\=\sqrt[3]{(-3)^6} $
Use the rule $\sqrt[n]{a^m} = a^{\frac{m}{n}}$ to obtain:
$=(-3)^{\frac{6}{3}}
\\=(-3)^2
\\=9$
