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Math Help - Express as a sum of terms of the form ax^r, where r is a rational number

  1. #1
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    Express as a sum of terms of the form ax^r, where r is a rational number

    The book lacks any explanation of how to do this or what it means.

    "Express as a sum of terms of the form ax^r, where r is a rational number"

    1. (4x^2 - x + 5) / x^(2/3)

    2. (x^2 + 2)^2 / x^5

    The answers given are:

    1. 4x^(4/3) - x^(1/3) + 5x^-(2/3)

    2. x^-1 + 4x^-3 + 4x^-5

    I haven't the faintest idea of how to begin this or how the answers were derived. Help would be appreciated.

    Thanks
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by sstecken View Post
    The book lacks any explanation of how to do this or what it means.

    "Express as a sum of terms of the form ax^r, where r is a rational number"

    1. (4x^2 - x + 5) / x^(2/3)

    2. (x^2 + 2)^2 / x^5

    The answers given are:

    1. 4x^(4/3) - x^(1/3) + 5x^-(2/3)

    2. x^-1 + 4x^-3 + 4x^-5

    I haven't the faintest idea of how to begin this or how the answers were derived. Help would be appreciated.

    Thanks
    1. \frac{4x^2-x+5}{x^{\tfrac{2}{3}}}

    All you need to do is rewrite this so each term has the form ax^r

    So...

    \frac{4x^2-x+5}{x^{\tfrac{2}{3}}}=4\frac{x^2}{x^{\tfrac{2}{3}  }}-\frac{x}{x^{\tfrac{2}{3}}}+5\frac{1}{x^{\tfrac{2}{  3}}}=\color{red}\boxed{4x^{\tfrac{4}{3}}-x^{\tfrac{1}{3}}+5x^{-\tfrac{2}{3}}}

    Does this make sense?

    Try the second one, and post what you did. Note that you will have to foil out the numerator first, and then split up the fraction.

    I hope this makes more sense to you now!

    --Chris
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    Awesome, makes perfect sense now. Thanks!
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