Today we were discussing exponents in math. One of the problems had "0" as an exponent, and the book didn't explain why the answer was "1." After thinking about it, I realized I didn't know "why" it was "1", either. I just knew that was a rule! So, I started looking for an explanation on the internet.
Homeschool Math Blog. She used patterns to explain why any number with 0 as an exponent is 1. (I like how she said that many books just "announce" that fact with no explanation. She calls it "announced mathematics.")
Basically, you can understand why a number with zero as an exponent is 1 by looking at the pattern. If you look at the pattern, you see you are dividing by 10 for each step. So, when you get to the last step, you get an answer of 1. So, 10 to the 0 power is 10 divided by 10, or 1. I think the photo explains it better than my explanation. Anyway, you can try it with any number as a base and you always would find that any number with an exponent of 0 is equal to 1.