# How do you write root4(16^3) as a fractional exponent?

$\sqrt[4]{{16}^{3}} = 8$
As $\sqrt[n]{a} = {a}^{\frac{1}{n}}$ and ${\left({a}^{m}\right)}^{\frac{1}{n}} = {a}^{\left(m \times \frac{1}{n}\right)} = {a}^{\frac{m}{n}}$
$\sqrt[4]{{16}^{3}} = {\left({16}^{3}\right)}^{\frac{1}{4}} = {\left({\left({2}^{4}\right)}^{3}\right)}^{\frac{1}{4}} = {2}^{\frac{4 \times 3}{4}}$
= ${2}^{\frac{12}{4}} = {2}^{3} = 8$