Dividing Exponents

Question

Hi! I was simplifying the problem 4^4/4^6
I tried ways of simplifying I learned in the lesson, and I got the answer 1/2 or 4^-2

The problem is, none of the choices I was given match those. I've tried redoing it several times, and I still get the same answer every time. The answer choices I was provided with are
-16
16
1/16
-1/16

I don't want the answer, but if anyone could tell me the method I should use to get one of the answers, I would really appreciate it.

Thank you!

Answer 1

First of all in your title, you are not dividing exponents, you are dividing powers.
4^4 / 4^6
= 4^-2 , using the rule: x^m ÷ x^n = x^(m-n)
= 1/4^2 , using the rule x^-n = 1/x^n

now what is 4^2 ????, that would be your denominator
The correct answer is there as a choice.

Answer 2

Thank you! That was really helpful!