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Math Help - Powers that are fractions?

  1. #1
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    Powers that are fractions?

    I have a question I'm not sure how to answer because I've never seen a power that is a fraction before. I need to simplify;

    x^(1/3) times x^(2/3)

    After some googling I think the fraction represents a cubed root, so the answer should be;

    cubed root of (x times x^2)

    Is that right?
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  2. #2
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    Re: Powers that are fractions?

    Yes.

    \sqrt[3]{x} \sqrt[3]{x^2} = \sqrt[3]{x*x^2} = x (for real x).
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  3. #3
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    Re: Powers that are fractions?

    Quote Originally Posted by Badgers View Post
    I have a question I'm not sure how to answer because I've never seen a power that is a fraction before. I need to simplify;

    x^(1/3) times x^(2/3)

    After some googling I think the fraction represents a cubed root, so the answer should be;

    cubed root of (x times x^2)

    Is that right?
    The index laws hold for powers that are ANY numbers, so you can use \displaystyle \begin{align*} a^m \cdot a^n = a^{m + n} \end{align*} to simplify.

    \displaystyle \begin{align*} x^{\frac{1}{3}} \cdot x^{\frac{2}{3}} &= x^{\frac{1}{3} + \frac{2}{3}} \\ &= x^1 \\ &= x \end{align*}
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  4. #4
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    Re: Powers that are fractions?

    Oh, rad! You guys are awesome! Thanks
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