Question

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

Answer 1

$2^{\frac{2}{3}}.2^{\frac{1}{5}}$

Sine we know that

$x^n.x^m=x^{(m+n)}$

$2^{\frac{2}{3}}.2^{\frac{1}{5}}=2^{\frac{2}{3}+\frac{1}{5}}$

Let's Solve the power as we have addition of unlike frcations

$\frac{2}{3}+\frac{1}{5}$

So, first find the lcm of 3 and 5, which would be 15

$=\frac{2\times 5+1\times 3}{15}$

$=\frac{10+3}{15}$

$=\frac{13}{15}$

Therefore, $2^{\frac{2}{3}+\frac{1}{5}}=2^{\frac{13}{15}}$

or we can say

$2^{\frac{2}{3}}.2^{\frac{1}{5}}=2^{\frac{13}{15}}$