How do you prove any number to the zero power is 1? like why is any number to the zero power one?

Step-by-step explanation:

It's a matter of being consistent in a pattern:

Let a be a number.  If a^(-3) is the first number, it's equal to 1 / a^3.

Next:

1 / a^2

1 / a^1

??                To fit into this pattern, a^0 must equal 1.

a^1

a^2

a^3

and so on.

Try this same exercise with a = 2:

2^(-2) = 1/4

2^(-1) = 1/2

??       This number has to be 1 to fit the pattern.  2^0 = 1.  Note that each

           term is 2x the previous term:  2(1/4) = 1/2; 2(1/2) = 1; 2(1) = 2; 2(2) = 4,

           and so on.  Again, 2^0 must = 1 to fit into this sequence.

2^1 = 2  

2^2 = 4