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Why do we need these rules?  Let's go back to an old example from rule #2:

w^3 / w^5 = w^(3-5) = w^(-2) = 1 / w^2

Look at this carefully...  It makes sense, doesn't it?  The problem was that the -2 exponent was confusing...  So, we need a way to deal with it.

Check out an example with just numbers:

2^(-3) = 1 / 2^3 = 1 / 8


TRY IT:

3^(-4) = _____     4^(-1) = _____     1 / 5^(-2) = _____


One of the games we'll be playing is to rewrite things so that there are no negative exponents.

Check it out:

-2 / w^(-3) = -2w^3
                      This negative is not effected!