The kid is learning about exponents, and I’m trying to help. 1/

One trick I think useful is to suggest he define, say, 4^3 not as 4 x 4 x 4, but as 1 x 4 x 4 x 4. Of course the two expressions amount to the same thing. But if you get into the habit of including the 1, it becomes obvious why 4^0 is just one. 2/

And since for positive exponents, subtracting an exponent corresponds to dividing by the base, you can just subtract past the zero exponent to define negative exponents. /fin