Question

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

Answer 1

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.

`= ((3(x^((1/3+(-2/3)))))/(3x^(-2/3)))`
`=((3x^(-1/3))/(3x^(-2/3)))`
divide the algebraic expression by 3.
next, we will use the first rule in the right column.
`(x^((-1/3-(-2/3)) ))`
finally, the answer will be;
`=x^(1/3) or 3sqrtx`

Explanation:

I hope you understood, if not follow what I did with the rules of indices to solve the problem.