Why every number to the power of 0 is equal to 1?

Question

I’m too dumb to get it

In: Mathematics

Answer 1

WE HAVE 13 axioms in number theory. Things that everyone agree are taken by true. They don’t need proof. There’s nothing magic about these axioms, other set could have been chosen. But it was decided to have those 13.

As an example, one of them is: x * 1 = x . This is accepted by a true not needed to be proved.

And you have de definition: x ^ y = x * x * x… * x a number of y times, right?

Now we have: x ^ (y+z) = x^y * (x^z). It can be proved by induction, but it makes sense by the above definition.

and x ^ (y-z) = x^y / x^z. It also can be proved by induction.

So x ^ (y-y) = x^y / x^y .

and you have

x^0 = 1.