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Math Help - Exponent simplification

  1. #1
    Junior Member Greymalkin's Avatar
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    Exponent simplification

    should be easy(for you):
    \frac{8}{27}(\frac{9}{4}x-\frac{5}{4})^\frac{3}{2}

    becomes

    \frac{1}{27}(9x-5)^\frac{3}{2}

    through what operations?
    Last edited by Greymalkin; November 19th 2012 at 07:42 AM.
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  2. #2
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    Re: Exponent simplification

    Quote Originally Posted by Greymalkin View Post
    should be easy(for you):
    \frac{8}{27}(\frac{9}{4}x-\frac{5}{4})^\frac{3}{2}

    becomes

    \frac{1}{27}(9x-5)^\frac{3}{2}

    through what operations?
    \displaystyle \begin{align*} \frac{8}{27} \left( \frac{9}{4} \, x - \frac{5}{4} \right) ^{\frac{3}{2}} &= \frac{8}{27} \left( \frac{9x - 5}{4} \right)^{\frac{3}{2}} \\ &= \frac{8}{27} \frac{\left( 9x - 5 \right)^{\frac{3}{2}}}{4^{\frac{3}{2}}} \\ &= \frac{8}{27} \frac{\left( 9x - 5 \right)^{\frac{3}{2}}}{\left( 4^{\frac{1}{2}} \right)^3} \\ &= \frac{8}{27} \frac{\left( 9x - 5 \right)^{\frac{3}{2}}}{2^3} \\ &= \frac{8}{27} \frac{\left( 9x - 5 \right)^{\frac{3}{2}}}{8} \\ &= \frac{1}{27} \left( 9x - 5 \right)^{\frac{3}{2}} \end{align*}
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  3. #3
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    Re: Exponent simplification

    Hi Grey.

    8/27 * (9/4 x - 5/4) ^ 3/2 =
    8/27 * [1/4 (9 x - 5)] ^ 3/2 =
    8/27 * (1/4) ^ 3/2 * (9 x - 5) ^ 3/2 =
    8/27 * 1/8 * (9 x - 5) ^ 3/2 =
    1/27 * (9 x - 5) ^ 3/2.

    Hope that helps. I'll learn to typeface soon. I'm still new to the forum.
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  4. #4
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    Re: Exponent simplification

    Quote Originally Posted by RBowman View Post
    Hi Grey.

    8/27 * (9/4 x - 5/4) ^ 3/2 =
    8/27 * [1/4 (9 x - 5)] ^ 3/2 =
    8/27 * (1/4) ^ 3/2 * (9 x - 5) ^ 3/2 =
    8/27 * 1/8 * (9 x - 5) ^ 3/2 =
    1/27 * (9 x - 5) ^ 3/2.

    Hope that helps. I'll learn to typeface soon. I'm still new to the forum.
    Hopefully you'll learn to type faster as well, I beat you by a full five minutes, even when using LaTeX :P lol
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  5. #5
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    Re: Exponent simplification

    I am a bit jealous. You wanna help by pointing me to best thread in the forum for users getting started with LaTeX? I'm also slow when it comes to finding things on my own.
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  6. #6
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    Re: Exponent simplification

    Look in the LaTeX help subforum on this site.
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  7. #7
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    Re: Exponent simplification

    Found it. Thanks Prove It.
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