Question

Solve
${\left(\frac{5}{3}\right)}^{-4}\times {\left(\frac{5}{3}\right)}^{-5}$

Answer 1

${\left(\frac{5}{3}\right)}^{-4}\times {\left(\frac{5}{3}\right)}^{-5}$

$={\left(\frac{5}{3}\right)}^{-4-5}$ since $a^m\times a^n=a^{m+n}$

$={\left(\frac{5}{3}\right)}^{-9}$

$={\left(\frac{3}{5}\right)}^9$ since $\frac{1}{a^m}=a^{-m}$

$=\frac{3^9}{5^9}$ since ${\left(\frac{a}{b}\right)}^m=\frac{a^m}{b^m}$

$=\frac{19683‬}{1953125‬}$