Question

Simplify:
$[{\left(\frac{1}{3}\right)}^{-3}-{\left(\frac{1}{2}\right)}^{-3}÷{\left(\frac{1}{5}\right)}^{-2}]$

Answer 1

$[{\left(\frac{1}{3}\right)}^{-3}-{\left(\frac{1}{2}\right)}^{-3}÷{\left(\frac{1}{5}\right)}^{-2}]$ $(\because {\left(\frac{a}{b}\right)}^m=\frac{a^m}{b^m})$
$[(\frac{1^{-3}}{3^{-3}}-\frac{1^{-3}}{2^{-3}})÷\frac{1^{-2}}{5^{-2}}]$
$(\because a^{-m}=\frac{1}{a^m})$
$[(\frac{3^3}{1^3}-\frac{2^{-3}}{1^3})÷\frac{5^{-2}}{1^2}]=(\frac{27}{1}-\frac{8}{1})÷25$
$=(27-8)÷25=\frac{19}{25}$