How do you simplify $343^{- \frac{4}{3}}$ $343^(-4/3)$ ?

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How do you simplify $343^{- \frac{4}{3}}$ $343^(-4/3)$ ?

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Answer 1 · 2018-04-07T13:24:23

$\frac{1}{2401}$ $1/2401$

Explanation:

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

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

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

$\Rightarrow 343^{- \frac{4}{3}} = \frac{1}{343^{\frac{4}{3}}}$ $rArr343^(-4/3)=1/343^(4/3)$

$343^{\frac{4}{3}} = {(\sqrt[3]{343})}^{4} = 7^{4} = 2401$ $343^(4/3)=(root(3)(343))^4=7^4=2401$

$\Rightarrow 343^{- \frac{4}{3}} = \frac{1}{2401}$ $rArr343^(-4/3)=1/2401$

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How do you simplify $343^{- \frac{4}{3}}$ $343^(-4/3)$ ?

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