How do you simplify $\frac{81^{\frac{3}{4}}}{81^{\frac{1}{4}}}$ $81^(3/4) / 81^(1/4)$ ?

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Answer 1 · 2018-04-17T03:21:08

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

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

$\frac{\sqrt[4]{81^{3}}}{\sqrt[4]{81}}$ $root(4)(81^3)/root(4)(81)$

So, we have,

$\sqrt[4]{\frac{81^{3}}{81}}$ $root(4)(81^3/81)$

Therefore, our result is,

$\sqrt[4]{81^{2}}$ $root(4)(81^2)$

$\Rightarrow \sqrt[4]{{(3^{4})}^{2}}$ $rArr root(4)((3^4)^2)$

$\Rightarrow 3^{\frac{8}{4}}$ $rArr 3^(8/4)$

$\Rightarrow 3^{2}$ $rArr 3^2$

$\Rightarrow 9$ $rArr 9$

Hope this helps :)

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