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Expressing fractions as powers?

  1. Dec 5, 2008 #1
    Expressing fractions as powers??

    How would you go about expressing this 127/squareroot(5) as a power of 5? I got a copy of last years exams to use for revision and practice and its full of stuff I don't know how to do. This one happens to be a multiple choice and the possible answers are 5 to the power of A:3 1/2, B: 6, C: -1 1/2, D: -3

    I know most of the laws of indices but im stuck here.
  2. jcsd
  3. Dec 5, 2008 #2
    Re: Expressing fractions as powers??

    Are you sure the question says 127/squareroot(5)?

    You can check that none of the answers match this value.
  4. Dec 5, 2008 #3


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    Re: Expressing fractions as powers??

    A number in the denominator corresponds to a number in the numerator with a negative power. However, sqrt(5) in the denominator is 5-1/2, not -1 1/2 or -3. If the denominator were [itex]\sqrt{5^3}= \sqrt{125}[/itex], then the exponent would be -3/2= -1 1/2.
  5. Dec 6, 2008 #4
    Re: Expressing fractions as powers??

    Sorry it was 125 over square root of 5 not 127. I have no idea how to solve this.

    I considered actually dividing the denominator into the numerator then using logs to convert the answer to a power of 5 but that method seems way too impractical to be the commonly used method.

    HallsofIvy I don't fully get what you said about the denominator and the numerator.
    Last edited: Dec 6, 2008
  6. Dec 6, 2008 #5
    Re: Expressing fractions as powers??

    Spelling it out,

    [tex]\frac{125}{\sqrt{5}} = \frac{5^3}{5^{1/2}} = 5^{3 - 1/2} = 5^{5/2}[/tex]
  7. Dec 7, 2008 #6
    Re: Expressing fractions as powers??

    Thanks a lot.
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