Question

Solve for x:

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

Answer 1

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

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

$[a^b={\left(\frac{1}{a}\right)}^{-b}]$

$\Rightarrow {\left(\frac{5}{3}\right)}^{-4-5}={\left(\frac{5}{3}\right)}^x$

Comparing powers: $x=-9$.