Evaluate

$\left(\frac{81}{49}\right)^{\frac{-3}{2}}=\left(\frac{49}{81}\right)^{\frac{3}{2}}$

$=\left(\frac{7^{2}}{9^{2}}\right)^{\frac{3}{2}}$

$=\left[\left(\frac{7}{9}\right)^{2}\right]^{\frac{3}{2}}$

$=\left(\frac{7}{9}\right)^{3}$

$=\frac{7^{3}}{9^{3}}$

$=\frac{343}{729}$

Hence, $\left(\frac{81}{49}\right)^{\frac{-3}{2}}=\frac{343}{729}$.