Question

Evaluate $\frac{{\left(36\right)}^{\frac{-7}{2}}-{\left(36\right)}^{\frac{-9}{2}}}{{\left(36\right)}^{\frac{-5}{2}}}.$

Answer 1

$\Rightarrow \frac{{36}^{\frac{-7}{2}}-{36}^{\frac{-9}{2}}}{{\left(36\right)}^{\frac{-5}{2}}}$
$\Rightarrow \frac{{\left(6\right)}^{2\times \frac{-7}{2}}-{\left(6\right)}^{2\times \frac{-9}{2}}}{{\left(6\right)}^{2\times \frac{-5}{2}}}$
$\Rightarrow \frac{6^{-7}-6^{-9}}{6^{-5}}$
$\Rightarrow \frac{6^{-7}}{6^{-5}}-\frac{6^{-9}}{6^{-5}}$
$=6^{-7+5}-6^{-9+5}$
$=6^{-2}-6^{-4}$
$=\frac{1}{6^2}-\frac{1}{6^4}$
$=\frac{6^2-1}{6^4}$