Answer
-3
Work Step by Step
As shown on page 445, we know that $a^{\frac{m}{n}}=\sqrt[n] a^{m}=(\sqrt[n] a)^{m}$.
Therefore, $(-27)^{\frac{1}{3}}=\sqrt[3] (-27)^{1}=\sqrt[3] -27=-3$.
We know that $\sqrt[3] -27=-3$, because $(-3)^{3}=-27$.