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Math Help - Trouble simplifing an exponental expression

  1. #1
    Newbie
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    Jan 2008
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    Smile Trouble simplifing an exponental expression

    Here's the expression that I'm having trouble with (sorry for the lack of ease of readability):

    ((2^-1)(x^-2)(y^-1))^-2((2x^-4)(y^3))^-2((16x^-3)(y^3))^0 / ((2x^-3)(y^-5))^2

    The answers is:

    x^18y^6 / 4

    I've worked this problem over and over as many different ways as I could, but I've never got the correct answer. I would appreciate very much it if someone could post the steps to solving this problem.

    Thanks for your time!
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  2. #2
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    Lexington, MA (USA)
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    Hello, ashepherd89!

    Simplify: . \frac{(2^{-1}x^{-2}y^{-1})^{-2}(2x^{-4}y^3)^{-2}(16x^{-3}y^3)^0} {(2x^{-3}y^{-5})^2}

    The answer is: . \frac{x^{18}y^6}{4}

    We have: . \frac{(2^{-1})^{-2}(x^{-2})^{-2}(y^{-1})^{-2}\cdot(2)^{-2}(x^{-4})^{-2}(y^3)^{-2}\cdot1} {2^2(x^{-3})^2(y^{-5})^2}

    . . = \;\frac{2^2x^4y^2\cdot2^{-2}x^8y^{-6}}{4x^{-6}y^{-10}} \;=\;\frac{x^{12}y^{-4}}{4x^{-6}y^{-10}} \;=\;\frac{x^{18}y^6}{4}

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  3. #3
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    Great! Thank you very much Soroban!
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