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