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

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

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Answer 1 · 2018-03-30T17:08:13

$27$ $27$

Explanation:

$using the law of exponents$ $"using the "color(blue)"law of exponents"$

$∙ x a^{\frac{m}{n}} = {(\sqrt[n]{a})}^{m}$ $•color(white)(x)a^(m/n)=(root(n)a)^m$

$\Rightarrow 81^{\frac{3}{4}} = {(\sqrt[4]{81})}^{3} = 3^{3} = 27$ $rArr81^(3/4)=(root(4)81)^3=3^3=27$

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

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