Answer
9
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, $(-243)^{\frac{2}{5}}=\sqrt[5] (-243)^{2}=(\sqrt[5] -243)^{2}=(-3)^{2}=9$.
We know that $\sqrt[5] -243=-3$, because $(-3)^{5}=-243$.
