Question

SImplify: $8^{{\log }_2(\sqrt[3]{3121}+\frac{1}{3})}$

Answer 1

let $y=8^{{\log }_{2}3\sqrt{121}+\frac{1}{3}}=2^{3[{\log }_2{121}^{1/3}+\frac{1}{3}]}$

$\Rightarrow y=2^{{\log }_{2}121+1}=2^{{\log }_{2}121}\left(2\right)=121\left(2\right)=242$