Simplifying with rational and negative exponents

  • Thread starter scarne92
  • Start date
  • #1
scarne92
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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
 

Answers and Replies

  • #2
36,338
8,295

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

Please verify that this is your expression (or not).

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
 
  • #3
scarne92
6
0
$$ \frac{3y^{1/3} - 3xy^{-2/3}2x}{y^{2/3}}$$

yes that is the expression, I couldn't get the LaTex to work properly, but yes.
 
  • #4
SHISHKABOB
541
1
$$ \frac{3y^{1/3} - 3xy^{-2/3}2x}{y^{2/3}}$$

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
 

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