Answer
$\frac{343}{125}$
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, $(\frac{49}{25})^{\frac{3}{2}}=(\sqrt \frac{49}{25})^{3}=(\frac{7}{5})^{3}=\frac{7}{5}\times\frac{7}{5}\times\frac{7}{5}=\frac{7\times7\times7}{5\times5\times5}=\frac{343}{125}$.
We know that $\sqrt \frac{49}{25}=\frac{7}{5}$, because $(\frac{7}{5})^{2}=\frac{49}{25}$
