# How do you simplify (3x^(1/3)*x^(-2/3))/(3x^(-2/3))?

Mar 11, 2018

When trying to solve this problem, you should think of the laws of indices. It will assist in solving this problem. Below is a picture of the laws.

So, let solve the problem.

so since x is the common term in the numerator we can use the third rule in the left column.

$= \left(\frac{3 \left({x}^{\left(\frac{1}{3} + \left(- \frac{2}{3}\right)\right)}\right)}{3 {x}^{- \frac{2}{3}}}\right)$
$= \left(\frac{3 {x}^{- \frac{1}{3}}}{3 {x}^{- \frac{2}{3}}}\right)$
divide the algebraic expression by 3.
next, we will use the first rule in the right column.
$\left({x}^{\left(- \frac{1}{3} - \left(- \frac{2}{3}\right)\right)}\right)$
$= {x}^{\frac{1}{3}} \mathmr{and} 3 \sqrt{x}$