Question

Simplify :$2^{\frac{2}{3}}\times 2^{\frac{1}{5}}$

Answer 1

Given $2^{\frac{2}{3}}\times 2^{\frac{1}{5}}$

$\begin{array}{c}{2}^{\frac{2}{3}}\times 2^{\frac{1}{5}}=2^{\frac{2}{3}+\frac{1}{5}}\mathbf{[}\mathbf{\therefore }{\mathit{a}}^{\mathbf{m}\mathbf{}}\mathbf{\times }{\mathit{a}}^{\mathbf{n}}\mathbf{}\mathbf{=}{\mathit{a}}^{\mathbf{m}\mathbf{+}\mathbf{n}}\mathbf{]}\\ =2^{\frac{10+3}{15}}\\ =2^{\frac{13}{15}}\end{array}$

Hence, the simplified form of $2^{\frac{2}{3}}\times 2^{\frac{1}{5}}$ is $2^{\frac{13}{15}}$.