Answer
$\frac{343}{125}$
Work Step by Step
$(\frac{25}{49})^{-\frac{3}{2}}=\frac{1}{(\frac{25}{49})^{\frac{3}{2}}}=\frac{1}{\sqrt((\frac{25}{49})^{3})}=\frac{1}{\sqrt(\frac{25}{49}\times \frac{25}{49}\times \frac{25}{49})}=\frac{1}{\sqrt(\frac{25}{49})\times \sqrt(\frac{25}{49})\times \sqrt(\frac{25}{49})}$
Further simplification:
$\frac{1}{\frac{5}{7}\times\frac{5}{7}\times\frac{5}{7}}=\frac{1}{\frac{125}{343}}=\frac{343}{125}$
We know that $\sqrt(\frac{25}{49})=\frac{5}{7}$, because $(\frac{5}{7})^{2}=\frac{25}{49}$.
