How would you explain to a 9th grader the negative exponent rule? Let us assume that the students haven't been exposed to these two rules: $a^{x+y} = a^{x}a^{y}$ and $\frac{a^x}{a^y} = a^{x-y}$. They have just been introduced to the generalization: $a^{-x} = \frac{1}{a^x}$ from the pattern method: $2^2 = 4, 2^1 = 2, 2^0 = 1, 2^{-1} = \frac{1}{2}$ etc. However, some students confuse $2^{-3}$ to be $(-2)(-2)(-2)$ since they are familiar with $2^{3} = 2 \cdot 2 \cdot 2$. This is a low-income urban school and most kids in this algebra class struggle with math dealing with exponents, fractions and decimals. What would be the best approach to reach all 32 students? 

I disagree with others saying that you need to teach the rule of 'flipping the number'. It may amount to this, but they need to know why first. Blindly learning rules puts a barrier in the place of deeper learning. Teach why then work through deducing the various rules with the students.
I think the answer from Jeppe was good - it builds on your existing answer, and using a physical example will help too. Just because the kids don't know some other 'rules' doesn't mean you can't teach this intuitively. In fact I think that this would be a good base for learning the two rules you quote.
(NOTE: this answer could probably have better been left as a couple of comments, but I am unfortunately low on rep on this stack-exchange site)
