# How do you write root3(125) in exponential form?

Jun 2, 2016

$\sqrt[3]{125} = {125}^{\frac{1}{3}}$

#### Explanation:

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

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

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

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

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