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Math Help - I need help with an experssion. Not sure under what category it falls.

  1. #1
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    I need help with an experssion. Not sure under what category it falls.

    1
    x^3


    I need to find the square root of the above equation.



    I found this in one of my homework questions and even after looking through all my notes I can't figure this one out. Can anyone perhaps get me started? I don't want to ask for the final answer because that wouldn't help me, but I'd very much appreciate a little bit of direction.
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  2. #2
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    Damn my lack of knowledge of these forums. The 1 is supposed to be above the x to the 3, as in a fraction.
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  3. #3
    Super Member Bacterius's Avatar
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    Don't worry, it is equivalent.

    So, you want to find \sqrt{\frac{1}{x^3}}. You can apply the rules of square roots, and we get :

    \sqrt{\frac{1}{x^3}} = \frac{\sqrt{1}}{\sqrt{x^3}}

    Now, \sqrt{1} = 1, so ...

    \sqrt{\frac{1}{x^3}} = \frac{1}{\sqrt{x^3}}

    Note that \sqrt{x^3} = (x^3)^{\frac{1}{2}}. By applying the laws of exponents, we have \sqrt{x^3} = (x^3)^{\frac{1}{2}} = x^{\frac{3}{2}}. Therefore :

    \sqrt{\frac{1}{x^3}} = \frac{1}{\sqrt{x^3}} = \frac{1}{x^{\frac{3}{2}}}

    If you wish to have a fraction-free result, remember that \frac{1}{a^b} = a^{-b}. Thus :

    \sqrt{\frac{1}{x^3}} = \frac{1}{\sqrt{x^3}} = \frac{1}{x^{\frac{3}{2}}} = x^{\frac{-3}{2}}.

    Does this make sense ? I tried to put as much help as I could, if you still have questions don't hesitate to ask. This can be applied to any such simplification problem.
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