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Math Help - Negative fractional indices

  1. #1
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    Negative fractional indices

    Rewrite x^(-3/2) without negative indices.

    I thought it would be x^(2/3)... why is this not correct?

    Also what is the difference between indices and exponents?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by olivia59 View Post
    Rewrite x^(-3/2) without negative indices.

    I thought it would be x^(2/3)... why is this not correct?

    Also what is the difference between indices and exponents?
    recall, x^{-a} = \frac 1{x^a} where x \ne 0

    now try again


    indices are exponents. just different names for the same thing. they are also called powers. ("indices" may refer to other things also, but here it means exponents)
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  3. #3
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    Quote Originally Posted by Jhevon View Post
    recall, x^{-a} = \frac 1{x^a} where x \ne 0

    now try again


    indices are exponents. just different names for the same thing. they are also called powers. ("indices" may refer to other things also, but here it means exponents)
    But I thought a 1/x was the same as the inverse. And inverse is the recipricol? And the recipricol of -3/2 is 2/3 is it not?
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  4. #4
    Super Member Quacky's Avatar
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    so would you say that \frac{-3}{2}=\frac{2}{3}?

    I think you are getting confused with what is meant by 'it becomes the inverse'. When the power is negative, it means that the 'x' (in this case) is the reciprocal.

    I've explained it very badly, so here are some examples.

    x^{-4}=\frac{1}{x^4}

    3^{-2}=\frac{1}{3^2}

    2x^{-5}=\frac{2}{x^5}

    It's probably easier to ignore the negative part to start with, and work out what it would look like just as a fractional power. Then take the reciprocal.

    Eg:

    x^{\displaystyle\frac{-5}{2}}

    So look at:

    x^{\displaystyle\frac{5}{2}}

    =\sqrt{x^5}

    Therefore:
    x^{\displaystyle\frac{-5}{2}}
     <br /> <br />
=\frac{1}{\sqrt{x^5}}<br />
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