Question

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

Answer 1

`root3 125 = 125^(1/3)`

Explanation:

You need to be aware that roots can be written as indices (exponents).
By definition, `rootn x = x^(1/n)" " eg. sqrtx = x^(1/2)`

This is then true for any root `rArr root3 x = x^(1/3)`

In this case `root3 125 = 125^(1/3)`

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

`root3 125 = root 3 5^3 = 5`