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Thread: Rationalize a fraction with fractional exponent

  1. #1
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    Rationalize a fraction with fractional exponent

    My question is, how are they getting from step 2 to step 3. Where is the 3^4/5 coming from?!

    Not sure i understand the rationalize the denominator of (1/3)^1/5

    Thanks for the help.
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  2. #2
    MHF Contributor
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    Re: Rationalize a fraction with fractional exponent

    You have \left( \frac{1}{3} \right)^\frac{1}{5} =  \frac{1^\frac{1}{5}}{3^\frac{1}{5}}  =  \frac{1}{3^\frac{1}{5}} and you want to get the fractional exponent out of the denominator. You can multiply top and bottom by whatever you like (except 0). Of course, you choose 3^{\frac{4}{5}} so that the denominator will be just 3. That's where 3^{\frac{4}{5}} comes from.

    And so you get  \frac{1}{3^\frac{1}{5}}  = \frac{3^{\frac{4}{5}}}{3^\frac{1}{5}3^{\frac{4}{5}  }}  =  \frac{3^\frac{4}{5}}{3}  =  \frac{1}{3} \, 3^\frac{4}{5}.

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