Question

Find the values of m and n if:

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

Answer 1

$4^{2m}=(\sqrt{8}{)}^2{4}^{2m}=8(2^2{)}^{2m}=2^3{2}^{4m}=2^{3}4m=3m=\frac{3}{4}$

$(\sqrt[3]{316}{)}^{-\frac{6}{n}}=(\sqrt{8}{)}^2\left[\right(16{)}^{\frac{1}{3}}{]}^{-\frac{6}{n}}=8\left[\right(2^4){]}^{-\frac{2}{n}}=2^3[2{]}^{-\frac{8}{n}}=2^3-\frac{8}{n}=3n=-\frac{8}{3}$