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Math Help - Why are these two expressions equivalent?

  1. #1
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    Why are these two expressions equivalent?

    Why are these two expressions equivalent?-screen-shot-2012-11-09-3.11.00-pm.png

    It's always fun when math text books just instruct you to 'observe' something without explaining it.

    Can someone break down for me why these two equal each other?
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: Why are these two expressions equivalent?

    If x^6-2=0 then you can rarrange to get x^6 = 2. Now take the 6th root of both sides:

     (x^6)^{1/6} = 2^{1/6}

     (x^6)^{1/6} = x^1 = x. This comes from the rule that ( x^a)^b = x^{(ab)}. So you have  x = 2^{1/6} or x = \sqrt[6] 2.

    Hence \sqrt[6]2 is a solution to x^6-2=0.
    Last edited by ebaines; November 9th 2012 at 11:27 AM.
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