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Homework Help: Simplifying with rational and negative exponents

  1. Sep 18, 2012 #1
    1. The problem statement, all variables and given/known data

    Simplify the expression completely

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

    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

    3√(3) y - 3√(6x) / y4

    3√3 - 3√6x / y3

    (3√3 - 3√6x / y3)3

    (3-6x) / y9
  2. jcsd
  3. Sep 19, 2012 #2


    Staff: Mentor

    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).
    It's not a good idea to convert to radicals at this point.
  4. Sep 19, 2012 #3
    $$ \frac{3y^{1/3} - 3xy^{-2/3}2x}{y^{2/3}}$$

    yes that is the expression, I couldn't get the LaTex to work properly, but yes.
  5. Sep 19, 2012 #4
    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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