#### Answer

$\frac{2}{3}$

#### 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, $(\frac{8}{27})^{\frac{1}{3}}=\sqrt[3] (\frac{8}{27})^{1}=\sqrt[3] (\frac{8}{27})=\frac{2}{3}$.
We know that $\sqrt[3] (\frac{8}{27})=\frac{2}{3}$, because $(\frac{2}{3})^{3}=\frac{2\times2\times2}{3\times3\times3}=\frac{8}{27}$.