Question

Simplify: ${\left(\frac{81}{16}\right)}^{-3/4}\times {\left(\frac{25}{9}\right)}^{-3/2}\times {\left(\frac{2}{5}\right)}^{-3}$

Answer 1

${\left(\frac{81}{16}\right)}^{-3/4}\times {\left(\frac{25}{9}\right)}^{-3/2}\times {\left(\frac{2}{5}\right)}^{-3}$

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

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

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

$={\left(\frac{30}{30}\right)}^{-3}$

$=1$.