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Thread: Simplify Equation

  1. #1
    Junior Member
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    Jul 2011
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    Simplify Equation

    Okay, I've been working on these problems for hours now and it has been killing me. I'm on the edge of. . . let me get to the point. . . Here's the problem.


    or the link
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    Here's what I gotten:

    $\displaystyle 27u^9/z^14$
    PLEASE ASSIST. I've tried.. Tried so much.. Wasted so many sheets of paper, this is ridiculous.
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  2. #2
    Super Member Quacky's Avatar
    Joined
    Nov 2009
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    Windsor, South-East England
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    901

    Re: Simplify Equation

    Take it one step at a time.

    Starting with:

    $\displaystyle (\frac{x^{-1}u^3}{3z^{-3}})$

    $\displaystyle x^{-1}=\frac{1}{x}$ and $\displaystyle z^{-3}=\frac{1}{z^3}$

    This means we can rewrite this as:

    $\displaystyle \frac{z^3u^3}{3x}$

    Cubing this:

    $\displaystyle [\frac{z^3u^3}{3x}]^3$

    $\displaystyle \frac{(z^3u^3)^3}{(3x)^3}$

    Take it one step at a time, starting with $\displaystyle (z^3)^3$

    $\displaystyle =(z^3)(z^3)(z^3)$

    =$\displaystyle z^9$ using the rule that $\displaystyle n^a\cdot{n^b}=n^{a+b}$

    We can generalize this to have:$\displaystyle (n^a)^b=n^{a\times{b}}$

    So do this to each term, remembering to cube the $\displaystyle 3$.

    Once you get there, it just becomes a case of cancelling.

    It looks like you're nearly finished with your simplifying. So no worries.
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