# How do you simplify 81^(3/4) / 81^(1/4) ?

Apr 17, 2018

${81}^{\frac{3}{4}} / {81}^{\frac{1}{4}}$

Law of indices states that ${a}^{\frac{m}{n}} = \sqrt[n]{{a}^{m}}$

$\frac{\sqrt[4]{{81}^{3}}}{\sqrt[4]{81}}$

So, we have,

$\sqrt[4]{{81}^{3} / 81}$

Therefore, our result is,

$\sqrt[4]{{81}^{2}}$

$\Rightarrow \sqrt[4]{{\left({3}^{4}\right)}^{2}}$

$\Rightarrow {3}^{\frac{8}{4}}$

$\Rightarrow {3}^{2}$

$\Rightarrow 9$

Hope this helps :)