Why the value of any nonzero number raised to the zero power equals 1?

Answer 1

One way to see this is as follows:

1. When you multiply numbers with the same base, you add the exponents (i.e., (a^x)*(a^y) = a^(x+y)).

2. a^(-x) = 1/a^(x). For example, 2^(-1) = 1/2.

Therefore,

(a^x)*(a^(-x)) = a^(x-x) = a^0 (from the first point above)

AND

(a^x)*(a^(-x)) = (a^x)*(1/(a^x)) = 1 (from the second point above)

So, (a^x)*(a^(-x)) equals both a^0 and 1, and therefore a^0 equals 1.