Answer
$\frac{1}{8}^{\frac{1}{3}}=\sqrt[3] \frac{1}{8}=\frac{1}{2}$
Work Step by Step
For all positive numbers $a$, where $a\ne1$, and all positive numbers $x$, we know that $y=log_{a}x$ means the same as $x=a^{y}$.
Therefore, $log_{\frac{1}{8}}\frac{1}{2}=\frac{1}{3}$ means the same as $\frac{1}{8}^{\frac{1}{3}}=\sqrt[3] \frac{1}{8}=\frac{1}{2}$.