Khan Academy

Supporting grades: 8

Description: Intuition on why a^(-b) = 1/(a^b) and why a^0 =1. Created by Sal Khan. I have been asked for some intuition as to why, let's say, a to the minus b is equal to 1 over a to the b. Well, what I'm going to show you is one of the reasons, and then we'll see that this is a good definition, because once you learned exponent rules, all of the other exponent rules stay consistent for negative exponents and when you raise something to the zero power. So the positive exponents, so you have a to the 1, a squared, a cubed, a to the fourth.

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