Answer
$\frac{64}{27}$
Work Step by Step
We know that $a^{\frac{m}{n}}=(\sqrt[n] a)^{m}$ (where m and n are positive integers greater than 1 with $\frac{m}{n}$ in simplest form and $\sqrt[n] a$ is a real number).
Therefore, $(\frac{16}{9})^{\frac{3}{2}}=(\sqrt \frac{16}{9})^{3}=(\frac{4}{3})^{3}=\frac{4}{3}\times\frac{4}{3}\times\frac{4}{3}=\frac{4\times4\times4}{3\times3\times3}=\frac{64}{27}$.
We know that $\sqrt \frac{16}{9}=\frac{4}{3}$, because $(\frac{4}{3})^{2}=\frac{16}{9}$
