Question

Simplify square root if 2 times the cubed root of 2

Answer 1

The exponent rule states that $a^{b} × a^{c} = a^{b+c}$.

$\sqrt[2]{2}~*~ \sqrt[3]{2}$ is equivalent to $2^{\frac{1}{2} }~*~2^{\frac{1}{3} }$.

You keep the coefficients the same, but add together the exponents.

$\frac{1}{2}~+~\frac{1}{3}~=~\frac{3}{6}~+~\frac{2}{6}~=~\frac{5}{6}$


$2^{ \frac{5}{6}}$
OR
$\sqrt[6]{2^{5}}$
OR
$\sqrt[6]{32}$. 

Answer 2

To simplify this, you need to apply the exponent rule; $a^{b} * a^{c} = a^{b + c}$. 

Your answer should be $2^{5/6}$.
Hope this helped!