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Simplify x^(n-1)⋅³√(y^2/2x^5) into Rationalised Surd Form

  1. Aug 22, 2015 #1
    1. The problem statement, all variables and given/known data
    a) Express [itex]x[/itex]^[itex](n-1)⋅³√(y^2/2x^5) [/itex] in its simplest, rationalised surd form.
    b) Given that the solution to part a) is 5, and that [itex]y[/itex] can be expressed as [itex]1/x[/itex]^[itex](6n+5)/4)[/itex], determine the value of [itex]x[/itex]. Again, express your answer in rationalised surd form.

    *Note, this is a non-calculator question*
    2. Relevant equations
    None, but I suppose knowledge of the index laws would be needed.

    3. The attempt at a solution
    I have attached my attempted workings to the sheet. While I believe to have gotten to a reasonable answer, I have no way of checking if I am right (this question has come from a sheet, not a text book). This is by far the hardest problem I've encountered with in dices thus far, so I would be very grateful if anybody could double check my work. Thank you for your time.

    Attached Files:

  2. jcsd
  3. Aug 22, 2015 #2


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    2017 Award

    Staff: Mentor

    You can plug your results in calculators like WolframAlpha to check them.
    I don't see obvious mistakes but checking the result with a computer is easier. Some steps look unnecessary.

    Edit: Oh, didn't check where the thread was.
    Last edited: Aug 22, 2015
  4. Aug 22, 2015 #3


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    Staff Emeritus
    Science Advisor
    Homework Helper

    You've posted a math problem in the Intro Physics HW forum, but I've moved to the Pre-Calculus HW forum, where it's a better fit.

    In the future, please try to post your HW questions in the appropriate HW forum by subject.
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