Hi Andretimpa...I think you got off topic with my question.

I was simply asking if for negative exponents: can I (1) define them (as my question stated), then (2) show continuity.

I had no problem proving from the definition that all other theorems of exponents could use negative exponents as well, but I was wondering if I am missing something by using this method of "define and show continuity"

Example:

I proved a^b * a^c = a^(b+c) WHEN b,c are both positive. Then I proved, after DEFINING negative exponents, that a^b * a^c = a^(b+c) even if b and/or c are negative.

I am simply asking if I this is okay.