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Math Help - simplify radicals with exponents

  1. #1
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    simplify radicals with exponents

    I had a real hard time with this problem and ended up getting it wrong, can someone point me in the right direction on how to solve it?

    (√y^5)/(3^√y^7)

    (note, by 3^√ I mean y^7 cubed)

    The answer should have been: 6^√y

    Attached an image to help make my question more clear.

    Thanks for any help offered!
    Attached Thumbnails Attached Thumbnails simplify radicals with exponents-q20.bmp  
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  2. #2
    MHF Contributor

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    What you have written is pretty much non-sense. Your 'clarification', "note, by 3^√ I mean y^7 cubed" just makes things worse (and your image does not show up). I suspect you meant "cube root", not "cubed". \sqrt[3]{y^7}= y^{7/3} and \sqrt{y^5}= y^{5/2}.

    \frac{\sqrt{y^5}}{\sqrt[3]{y^7}}= \frac{y^{5/2}}{y^{7/3}}= y^{5/2- 7/3}= y^{1/6}= \sqrt[6]{y}.
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  3. #3
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    I'm not sure why the image does not show, I can see it as an attached image, but yes, I meant cubed root. I was getting frustrated on making [tex] work with root equations, but now I see how to do that too. Much easier than expected, not sure how I overlooked that, thank you for your help!
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