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Math Help - Properites of Derivatives question about the power rule

  1. #1
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    Question Properites of Derivatives question about the power rule

    Hi I have this question:

    \sqrt{4x^3}

    so I cann use the power rule to rewrite this question correct? so it would be like so:

     2\sqrt{x^3}

    It is the next step I'm confused about.

     2(x^3)^\frac{1}{ 2}

    how do you get the 1/2 exponent?
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    Quote Originally Posted by sara213 View Post
    Hi I have this question:

    \sqrt{4x^3}

    so I cann use the power rule to rewrite this question correct? so it would be like so:

     2\sqrt{x^3}

    It is the next step I'm confused about.

     2(x^3)^\frac{1}{ 2}

    how do you get the 1/2 exponent?

    Hello Sara.



    \sqrt[n]{x^m}=x^{\frac{m}{n}}

    and:

    (x^a)^b=x^{ab}
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  3. #3
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    This is simply the definition of square root. An nth root is simply the exponent 1/n.
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  4. #4
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    you know i kind of feel stupid to ask that question...because I knew that....sorry guys...><

    but I think i just needed confirmation is all. thanks
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