## Intermediate Algebra for College Students (7th Edition)

$9$
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: $=(-3)^{\frac{6}{3}} \\=(-3)^2 \\=9$