Question

Evaluate ${\left(\frac{5}{8}\right)}^{-7}\times {\left(\frac{8}{5}\right)}^{-4}$ is $\frac{512}{m}$
Value of $m$ is

Answer 1

Formulae to be used :
$a^m\times a^n=a^{m+n}$
$a^{-n}=\frac{1}{a^n}$
$(\frac{5}{8}{)}^{-7}\times (\frac{5}{8}{)}^4=(\frac{5}{8}{)}^{4-7}=(\frac{5}{8}{)}^{-3}=(\frac{8}{5}{)}^3=\frac{512}{125}$