Simplify ${(\frac{81}{16})}^{- \frac{3}{9}}$ $(81/16)^(-3/9)$ ?

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Simplify ${(\frac{81}{16})}^{- \frac{3}{9}}$ $(81/16)^(-3/9)$ ?

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Answer 1 · 2018-04-27T11:08:36

$\frac{\sqrt[3]{16}}{\sqrt[3]{81}}$ $(root(3)(16))/(root(3)(81))$

Explanation:

$note that - \frac{3}{9} = - \frac{1}{3}$ $"note that "-3/9=-1/3$

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

$∙ x a^{- m} \Leftrightarrow \frac{1}{a^{m}}$ $•color(white)(x)a^-mhArr1/a^m$

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

$\Rightarrow {(\frac{81}{16})}^{- \frac{1}{3}}$ $rArr(81/16)^(-1/3)$

$= \frac{1}{{(\frac{81}{16})}^{\frac{1}{3}}} = \frac{1}{\frac{\sqrt[3]{81}}{\sqrt[3]{16}}} = \frac{\sqrt[3]{16}}{\sqrt[3]{81}}$ $=1/(81/16)^(1/3)=1/(root(3)(81)/root(3)(16))=(root(3)(16))/(root(3)(81)$

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Simplify ${(\frac{81}{16})}^{- \frac{3}{9}}$ $(81/16)^(-3/9)$ ?

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Simplify ${(\frac{81}{16})}^{- \frac{3}{9}}$ $(81/16)^(-3/9)$ ?