Question

Simplify : ${\left(\frac{5}{8}\right)}^{-7}\times {\left(\frac{8}{5}\right)}^{-4}$

Answer 1

Let $a={\left(\frac{5}{8}\right)}^{-7}\times {\left(\frac{8}{5}\right)}^{-4}$

$={\left(\frac{8}{5}\right)}^7\times {\left(\frac{8}{5}\right)}^{-4}$ [$\because {\left(\frac{a}{b}\right)}^{-1}$= $\frac{b}{a}$]

$={\left(\frac{8}{5}\right)}^{7-4}$ [ $\because a^m+a^n=a^{m+n}$ ]

$={\left(\frac{8}{5}\right)}^3$

$\therefore$ $a=\frac{512}{125}$