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Math Help - Simplify fraction exponents

  1. #1
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    Simplify fraction exponents

    Hey everyone, I am typically very good at math; however, I have always struggled with fractions. I am currently reviewing pre-calculus so that I can test out of pre-calc for my accounting degree. I have a problem on my review work that I have been attempting to solve and just cannot get it.... I am really hoping someone could walk me through this... Thanks in advance!

    (49x-2y4)-1/2(xy1/2)

    I can get to what I'm 99% sure is the next step...

    [x√(y)]
    [√(49) √(x-2) √(y4)]

    Followed by... (which I'm not as sure is correct)

    x √(y)
    7 √(x-2) y2

    And this is where I get stuck... I'm not sure what to do with the negative exponent in the denominator... If someone could explain the next step for me, I would greatly appreciate it.
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  2. #2
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    Re: Simplify fraction exponents

    Simplify fraction exponents-02-jul-13.png
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  3. #3
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    Re: Simplify fraction exponents

    Hello, Cyryn!

    \text{Simplify: }\:\left(49x^{\text{-}2}y^4\right)^{\text{-}\frac{1}{2}}\left(xy^{\frac{1}{2}}\right)

    First of all, avoid radicals . . . until the very end.

    We have: . \left(49x^{\text{-}2}y^4\right)^{\text{-}\frac{1}{2}}\left(xy^{\frac{1}{2}}\right)

    . . . . . . =\;\big(49\big)^{\text{-}\frac{1}{2}}\left(x^{\text{-}2}\right)^{\text{-}\frac{1}{2}}\left(y^4\right)^{\text{-}\frac{1}{2}}\left(xy^{\frac{1}{2}}\right)

    . . . . . . =\; \left(7^2\right)^{\text{-}\frac{1}{2}} \big(x^1\big)\big( y^{\text{-}2}\big) \cdot x \cdot y^{\frac{1}{2}}

    . . . . . . =\; 7^{\text{-}1}\big(x\cdot x\big)\left(y^{\text{-}2}\cdot y^{\frac{1}{2}}\right)

    . . . . . . =\;7^{\text{-}1}\cdot x^2\cdot y^{\text{-}\frac{3}{2}}

    . . . . . . =\;\frac{1}{7}\cdot x^2\cdot \frac{1}{y^{\frac{3}{2}}}

    . . . . . . =\;\frac{x^2}{7\sqrt{y^3}}
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  4. #4
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    Re: Simplify fraction exponents

    Thank you, thank you, thank you!!! The examples in my book were putting things into radicals early which I think is where I'm getting confused, but how you did it makes so much more sense! Thanks sooooo much.
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