# How do you write (16a^6)^(3/4) in radical form?

Jun 25, 2016

$8 {a}^{4} \sqrt{a}$

#### Explanation:

An index which is a fraction is made up of 2 parts - a root and a power.

${\left(16 {a}^{6}\right)}^{\frac{3}{4}}$ can be written as ${\sqrt[4]{\left(16 {a}^{6}\right)}}^{3}$

=${\sqrt[4]{16}}^{3} \times {\sqrt[4]{{a}^{6}}}^{3}$

=${2}^{3} \times {a}^{\frac{18}{4}}$
=$8 \times {a}^{\frac{9}{2}} = 8 \times {a}^{\frac{8}{2}} \times {a}^{\frac{1}{2}}$

=$8 {a}^{4} \sqrt{a}$