How do you simplify (4^(1/3))^(3/2)?

Feb 1, 2017

$= \pm 2$

Explanation:

${\left({4}^{\frac{1}{3}}\right)}^{\frac{3}{2}}$

$= {4}^{\frac{1}{3} \times \frac{3}{2}}$

$= {4}^{\frac{1}{2}}$

$= \sqrt{4}$

$= \pm 2$

Feb 1, 2017

See the entire simplification process below:

Explanation:

First, use this rule for exponents to start the simplification process:

${\left({x}^{\textcolor{red}{a}}\right)}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} \times \textcolor{b l u e}{b}}$

${\left({4}^{\textcolor{red}{\frac{1}{3}}}\right)}^{\textcolor{b l u e}{\frac{3}{2}}} = {4}^{\textcolor{red}{\frac{1}{3}} \times \textcolor{b l u e}{\frac{3}{2}}} = {4}^{\frac{3}{6}} = {4}^{\frac{1}{2}} = 2$