>Something raised to the power of 0 is not equal to 0 Why

If you do the problems from the first chapter of small rudin they give a lot of insight into this :)

>>9155020
Repeated addition(Multiplication) needs an additive identity (0) to be done right.
Why? Because you need some beginning number(0) to add all those others to, so you have the case for multiplying by 0.
3*4=0+3+3+3+3
3*0=0
Repeated multiplication(Exponentiation) needs a multiplicative identity (1) to be done right.
Why?
Because you need some beginning number(1) to multiply all those others to, so you have the case for exponentiating by 0.
3^4=1*3*3*3*3
3^0=1

>>9155037
Oh wow I actually get it now. My math teacher didn't even bother explaining it, even when asked.

>>9155037
this post is succinct and informative

3^n = 3^(n+1) / 3

3^0 = 3^(1) / 3 = 3 / 3 = 1

>>9155037
So I heard a bunch of people say that it's a mistake to consider multiplication in its most general conception as repeated addition.

Here's an example https://www.maa.org/external_archive/devlin/devlin_06_08.html

I can't find it, but this one mathemetitian published some papers addressed to teachers calling for a stop to that approach despite its usefulness