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Math Help - properties of exponents to simplify expressions. help needed.

  1. #1
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    properties of exponents to simplify expressions. help needed.

    hello there. so i took precalculus in 10th grade, like 3 years ago, and now it's coming back to haunt me on my math placement for college which i have to take in a few days. I'm having a hard time remembering things so if someone could just please help me out i'd greatly appreciate it.

    use the properties of exponents to simplify the expression:




    i already know the answer is Y/X, but i don't know how to get it.
    Last edited by rafaeli; June 29th 2008 at 09:43 AM.
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  2. #2
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    Quote Originally Posted by rafaeli View Post
    hello there. so i took precalculus in 10th grade, like 3 years ago, and now it's coming back to haunt me on my math placement for college which i have to take in a few days. I'm having a hard time remembering things so if someone could just please help me out i'd greatly appreciate it.

    use the properties of exponents to simplify the expression:

    {X^(3/4), Y^(1/2)}
    ------------------- that whole expression raised to the -2.
    X^(1/4), Y


    i already know the answer is Y/X, but i don't know how to get it.
    \left(\dfrac{x^{\frac34} y^{\frac12}}{x^{\frac14}y}\right)^{-2}

    Use the rule \frac{x^a}{x^b} = x^{a-b},

    \left(\dfrac{x^{\frac34} y^{\frac12}}{x^{\frac14}y}\right)^{-2}  = (x^{\frac34- \frac14} y^{\frac12 - 1})^{-2} = (x^{\frac12} y^{-\frac12})^{-2} = \left(\frac{x^{\frac12}}{y^{\frac12}}\right)^{-2}

    Now lets use the rule \frac{x^a}{y^a}  = \left(\frac{x}{y}\right)^a

    \left(\frac{x^{\frac12}}{y^{\frac12}}\right)^{-2}= \left(\left(\frac{x}{y}\right)^{\frac12}\right)^{-2}

    And finally lets use the rule: (x^a)^b = x^{ab}

    \left(\left(\frac{x}{y}\right)^{\frac12}\right)^{-2} =\left(\frac{x}{y}\right)^{-2 . \frac12}=\left(\frac{x}{y}\right)^{-1} = \frac{y}{x}
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