Question

Simplify:
${\{{\left(\frac{3}{4}\right)}^{-1}-{\left(\frac{1}{4}\right)}^{-1}\}}^{-2}$

Answer 1

Consider ${\left(\frac{3}{4}\right)}^{-1}-{\left(\frac{1}{4}\right)}^{-1}$

$=\frac{4}{3}-4$ Since $\frac{1}{a^{-m}}=a^m$

$=\frac{4-12}{3}=\frac{-8}{3}$

Again ${({\left(\frac{3}{4}\right)}^{-1}-{\left(\frac{1}{4}\right)}^{-1})}^{-2}$

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

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

$=\frac{9}{64}$