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Math Help - Roots expressed as exponents question

  1. #1
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    Roots expressed as exponents question

    Hello, the author seems to contradict herself in the following examples. See below

    This Is correct
    Expression 1:



    Expression 2:
    I think the author did this incorrectly
    \sqrt[4]{x^3}=x^{3/4}

    If we follow the logic of expression 1 should it should be \sqrt[4]{x^3}=(x^3)^{1/4}

    Could someone please verify this seemingly contradictory expression?
    Thanks
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  2. #2
    MHF Contributor red_dog's Avatar
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    It's correct because (x^3)^{\frac{1}{4}}=x^{3\cdot\frac{1}{4}}=x^{\frac  {3}{4}}
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  3. #3
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    Well if thats the case could we take


    = 3xy^{(7\cdot\frac{-1}{5})}
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  4. #4
    MHF Contributor red_dog's Avatar
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    Quote Originally Posted by allyourbass2212 View Post
    Well if thats the case could we take


    = 3xy^{(7\cdot\frac{-1}{5})}
    No.

    (3xy^7)^{-\frac{1}{5}}=3^{-\frac{1}{5}}x^{-\frac{1}{5}}y^{-\frac{7}{5}}

    Remember that (ab)^n=a^nb^n
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