# Simplifying with rational and negative exponents

## Homework Statement

Simplify the expression completely

3(y)(1/3)-3x(y)(-2/3)(2x) / [(y)(1/3)]2

## The Attempt at a Solution

My attempt is totally wrong. I can't quit figure out what to do or where to start

3(y)(1/3)-3x(y)(-2/3)(2x) / [(y)(1/3)]2

3(y)(1/3)-6x(y)(-2/3) / y(2/3)

3√[3(y)(1/3)-6x(y)(-2/3) / y(2/3)]

3√(3) y - 3√(6x) y-2 / y2

3√(3) y - 3√(6x) / y4

3√3 - 3√6x / y3

(3√3 - 3√6x / y3)3

(3-6x) / y9

Mark44
Mentor

## Homework Statement

Simplify the expression completely

3(y)(1/3)-3x(y)(-2/3)(2x) / [(y)(1/3)]2
Although you have used lots of parentheses, for which you are to be applauded, you might be missing the most important pair.

It looks like this is the expression you need to simplify:
$$\frac{3y^{1/3} - 3xy^{-2/3}2x}{y^{2/3}}$$
Or, without using LaTeX:
[3y1/3 - 3xy-2/32x]/y2/3

## The Attempt at a Solution

My attempt is totally wrong. I can't quit figure out what to do or where to start

3(y)(1/3)-3x(y)(-2/3)(2x) / [(y)(1/3)]2

3(y)(1/3)-6x(y)(-2/3) / y(2/3)

3√[3(y)(1/3)-6x(y)(-2/3) / y(2/3)]

3√(3) y - 3√(6x) y-2 / y2
It's not a good idea to convert to radicals at this point.
3√(3) y - 3√(6x) / y4

3√3 - 3√6x / y3

(3√3 - 3√6x / y3)3

(3-6x) / y9

$$\frac{3y^{1/3} - 3xy^{-2/3}2x}{y^{2/3}}$$

yes that is the expression, I couldn't get the LaTex to work properly, but yes.

$$\frac{3y^{1/3} - 3xy^{-2/3}2x}{y^{2/3}}$$

yes that is the expression, I couldn't get the LaTex to work properly, but yes.

looks like if you try separating them like this

$$\frac{3y^{1/3}}{y^{2/3}} - \frac{3xy^{-2/3}2x}{y^{2/3}}$$

it should work out a bit better