#### Answer

$\frac{8}{9}$

#### 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, $(\frac{64}{81})^{\frac{1}{2}}=\sqrt[2] (\frac{64}{81})^{1}=\sqrt (\frac{64}{81})=\frac{8}{9}$.
We know that $\sqrt (\frac{64}{81})=\frac{8}{9}$, because $(\frac{8}{9})^{2}=(\frac{64}{81})$.