Question

Simply
${\left(\frac{81}{16}\right)}^{-3/4}\times {\left(\frac{25}{9}\right)}^{\frac{-3}{2}}$

Answer 1

${\left(\frac{81}{16}\right)}^{\frac{-3}{4}}\times {\left(\frac{25}{9}\right)}^{\frac{-3}{2}}$

$={\left(\frac{3}{2}\right)}^{4\times \frac{-3}{4}}\times {\left(\frac{5}{3}\right)}^{2\times \frac{-3}{2}}$

$={\left(\frac{3}{2}\right)}^{-3}\times {\left(\frac{5}{3}\right)}^{-3}={\left(\frac{5}{2}\right)}^{-3}={\left(\frac{2}{5}\right)}^3=\frac{8}{125}$