Answer
-4
Work Step by Step
We are given that $a^{\frac{m}{n}}=\sqrt[n] a^{m}=(\sqrt[n] a)^{m}$, if all indicated roots are real numbers.
Therefore, $-8^{\frac{2}{3}}=-(8^{\frac{2}{3}})=-(\sqrt[3] 8^{2})=-[(\sqrt[3] 8)^{2}]=-[(2)^{2}]=-[4]=-4$.
We know that $\sqrt[3] 8=2$, because $2^{3}=8$.