1. 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.

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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.

2. 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.