Question

Find the value of m and n if
$4^{2m}={\left(\sqrt[3]{316}\right)}^{-\frac{6}{n}}={\left(\sqrt{8}\right)}^2$

Answer 1

$4^{2m}=(\sqrt[3]{316}{)}^{-\frac{6}{n}}=(\sqrt{8}{)}^2$

$2^{4m}=2^{-\frac{8}{n}}=2^3$

$⟹m=\frac{3}{4},n=-\frac{8}{3}$