Question about dividing numbers and variables that have powers?

Ok.. Laws of Exponents says: (A^B)/(A^C) = A^(B-C), but then I read this:





If a variable's power is greater in the denominator, then the difference between the two powers is written as a positive power of the base -- in the denominator.





Basically, they contradict each other.. and I know negative exponents exist.. Negative exponents would never exist if you always wrote them as a positive power. Does this mean negative exponents only exist in the numerator when subtracting powers?Question about dividing numbers and variables that have powers?
Basically, what it's telling you is that A^(-B) = 1/(A^B).





So, say, if you have 9^5/9^7, this could be written as 9^(-2), which is the same thing as writing 1/(9^2).