How do you simplify 5x^(2/3)?

Aug 26, 2015

color(green)(5* root(3)(x^2)

Explanation:

This cannot really be simplified further, but it can be written in a form which is easier to understand.

A property of exponents says that :
color(blue)((a)^(m/n) = (a^m)^(1/n)

Hence $5 {x}^{\frac{2}{3}}$ can be written as $5 \cdot {\left({x}^{2}\right)}^{\frac{1}{3}}$

Also color(blue)(a^(1/n) = root(n)(a)

Hence $5 \cdot {\left({x}^{2}\right)}^{\frac{1}{3}}$ = color(green)(5* root(3)(x^2)