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Help with simplification

  1. May 4, 2014 #1
    1. The problem statement, all variables and given/known data
    Om a > 0, b > 0, c > 0, och x = ((ab√c)1/3-a(b2c)1/4)/(a3b2c)1/6

    3. The attempt at a solution

    I have no idea where to start. I understand the relevance of a,b and c being > 0 in order to simplify but other than that I am pretty much stuck!
     
  2. jcsd
  3. May 4, 2014 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    A first obvious step is to replace that [itex]\sqrt{c}[/itex] with [itex]c^{1/2}[/itex]. Then use the "laws of exponentials: [itex](abc^{1/2})^{1/3}= a^{1/3}b^{1/3}c^{1/6}[/itex], [itex]a(b^2c)^{1/4}= ab^{1/2}c^{1/4}[/itex] and [itex](a^3b^2c)^{1/6}= a^{1/2}b^{1/3}c^{1/6}[/itex]

    So you have [tex]\frac{a^{1/3}b^{1/3}c^{1/6}- ab^{1/2}c^{1/4}}{a^{1/2}b^{1/3}c^{1/6}}[/tex]

    Factor the largest power of a, b, and c in both terms in the numerator and cancel what you can with the denominator.
     
  4. May 4, 2014 #3
    \begin{align*}
    \frac{\sqrt[3]{ab \sqrt{c}} - a \sqrt[4]{b^2 c}}{\sqrt[6]{a^3 b^2 c}}
    \end{align*}

    Wrote the equation in latex too, it was easier to see.
     
  5. May 4, 2014 #4
    Alright that was easier than I previously thought! Thanks!
     
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