# How do you simplify 16^(2/3)?

Mar 7, 2016

${16}^{\frac{2}{3}} = 4 \sqrt[3]{4}$

#### Explanation:

A fractional exponent with $n$ in the denominator is equivalent to taking the ${n}^{\text{th}}$ root of the base. Then, together with the property that ${x}^{a b} = {\left({x}^{a}\right)}^{b}$ we have

${16}^{\frac{2}{3}} = {\left({16}^{2}\right)}^{\frac{1}{3}}$

$= \sqrt[3]{256}$

$= \sqrt[3]{{4}^{3} \cdot 4}$

$= 4 \sqrt[3]{4}$