Question

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

Answer 1

$\frac{25}{4}=\frac{5\times 5}{2\times 2}=\frac{5^2}{2^2}$
${\left(\frac{2}{5}\right)}^{-3}\times {\left(\frac{25}{4}\right)}^{-2}={\left(\frac{2}{5}\right)}^{-3}\times {\left(\frac{5^2}{2^2}\right)}^{-2}$
$(\because {\left(a^m\right)}^n=a^{mn})$
$\frac{5^3}{2^3}\times \frac{2^4}{5^4}=5^{3-4}\times 2^{4-3}$
As $(\because a^{-m}=\frac{1}{a^m})$
$=5^{-1}\times 2^1=\frac{2}{5}$