Comment by jkent

I successfully managed to explain 3^0 to 10 year olds (as a recovering high school math teacher) as:

  3^2 = 9
  3^1 = 3  (divide 9 by 3)
  3^0 = 1  (divide 3 by 3)
  3^-1 = 1/3  (divide 1 by 3)
  etc

This can logically be explained as n^0=1 for all real numbers.

Unfortunately this doesn't really handle 0^0 but fortunately 10 year olds are rarely that difficult.