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

Given: $2^{\frac{2}{3}}\times 2^{\frac{1}{3}}$.

To do: Simplify: $2^{\frac{2}{3}}\times 2^{\frac{1}{3}}$.

Solution: 

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

$=2^{\frac{2}{3}+\frac{1}{3}}$                     [$\because\ a^m\times a^n=a^{m+n}$]

$=2^{\frac{2+1}{3}}$

$=2^{{3}{3}}$

$=2^1$

$=2$ 

Thus, $2^{\frac{2}{3}}\times 2^{\frac{1}{3}}=2$.

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Updated on: 10-Oct-2022

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