How do you write $\sqrt[3]{125}$ $root3(125)$ in exponential form?

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How do you write $\sqrt[3]{125}$ $root3(125)$ in exponential form?

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Answer 1 · 2016-06-02T12:05:46

$\sqrt[3]{125} = 125^{\frac{1}{3}}$ $root3 125 = 125^(1/3)$

Explanation:

You need to be aware that roots can be written as indices (exponents).
By definition, $\sqrt[n]{x} = x^{\frac{1}{n}} e g . \sqrt{x} = x^{\frac{1}{2}}$ $rootn x = x^(1/n)" " eg. sqrtx = x^(1/2)$

This is then true for any root $\Rightarrow \sqrt[3]{x} = x^{\frac{1}{3}}$ $rArr root3 x = x^(1/3)$

In this case $\sqrt[3]{125} = 125^{\frac{1}{3}}$ $root3 125 = 125^(1/3)$

This is now written in the required form, but it can be simplified
to give an answer of 5.

$\sqrt[3]{125} = {\sqrt[3]{5}}^{3} = 5$ $root3 125 = root 3 5^3 = 5$

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How do you write $\sqrt[3]{125}$ $root3(125)$ in exponential form?

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