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Math Help - Simplifying exponential equations

  1. #1
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    Simplifying exponential equations

    Ok, here are the two equations I can't seem to solve.

    10x^-3 * (5x^-2)^-3/2^4 * x^(3/2)

    and

    6p^-4 * (4p^3)^-1/p^-5

    The answers are x^(3/2)/200 for the first equation and 3/2p^2 for the second equation.

    However, I keep coming up with -1250x^(3/2)/16 for the first equation and 1/24p^2 for the second equation. I have a test monday and I need to know how to do these problems...they're frusterating.
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by some_nerdy_guy View Post
    Ok, here are the two equations I can't seem to solve.

    10x^-3 * (5x^-2)^-3/2^4 * x^(3/2)

    and

    6p^-4 * (4p^3)^-1/p^-5

    The answers are x^(3/2)/200 for the first equation and 3/2p^2 for the second equation.

    However, I keep coming up with -1250x^(3/2)/16 for the first equation and 1/24p^2 for the second equation. I have a test monday and I need to know how to do these problems...they're frusterating.
    Aa^n\cdot Ba^m\cdot Ca^p = ABCa^{n+m+p} and any coefficients are multiplied together

    \frac{10x^{-3} \cdot (5x^{-2})^{-3}}{2^4 \cdot x^{\frac{3}{2}}}

    (5x^{-2})^{-3} = \frac{x^6}{125}


    \frac{10x^{-3} \cdot \frac{x^6}{125}}{2^4 \cdot x^{\frac{3}{2}}} = \frac{\frac{2x^3}{25}}{16x^{\frac{3}{2}}}

    = \frac{x^{\frac{3}{2}}}{200}
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  3. #3
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by some_nerdy_guy View Post
    Ok, here are the two equations I can't seem to solve.

    10x^-3 * (5x^-2)^-3/2^4 * x^(3/2)

    and

    6p^-4 * (4p^3)^-1/p^-5

    The answers are x^(3/2)/200 for the first equation and 3/2p^2 for the second equation.

    However, I keep coming up with -1250x^(3/2)/16 for the first equation and 1/24p^2 for the second equation. I have a test Monday and I need to know how to do these problems...they're frustrating.

    Formula:


    • \frac{x^{a}}{x^{b}} =x^{a-b}
    • x^{a} \times x^b = x^{a+b}
    • (x^a)^b = x^{ab}


    1) 10x^-3 * (5x^-2)^-3/2^4 * x^(3/2)

    \frac{10 x^{-3} \times (5 x^{-2})^{-3}}{2^4 \times x^{3/2}}


    \frac{10 x^{-3} \times ( x^{6})}{2^4 \times x^{3/2}\times 125}

    \frac{ x^{-3+6} }{16 \times x^{3/2}\times 125}

    \frac{ x^{3} }{2000 \times x^{3/2}}

    \frac{ x^{3-\frac{3}{2}} }{200 }


    \frac{ x^{\frac{3}{2}} }{200 }

    ---------------------------------------------------------------
    2) 6p^-4 * (4p^3)^-1/p^-5
    <br />
\frac{6 p^{-4} \times (4p^3)^{-1}}{p^{-5}}

    \frac{6 p^{-4} \times (p^{-3})}{4 \times  p^{-5}}

    \frac{6 p^{-4-3} }{4 \times  p^{-5}}

    \frac{6 p^{-4-3-(-5)} }{4 }

    \frac{6 p^{-2} }{4 }

    \frac{3 }{2p^2 }
    Last edited by ADARSH; March 14th 2009 at 12:38 PM.
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