Question

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

Answer 1

Given ${\{{\left(\frac{1}{3}\right)}^{-1}-{\left(\frac{1}{4}\right)}^{-1}\}}^{-1}={\{{\left(\frac{3}{1}\right)}^1-{\left(\frac{4}{1}\right)}^1\}}^{-1}[\because (\frac{a}{b}{)}^{-m}=\left(\frac{b}{a}{)}^m\right]={\{3-4\}}^{-1}={\{-1\}}^{-1}=-1$