eli5: why is x⁰ = 1 instead of non-existent?

Question

It kinda doesn’t make sense.
x¹= x

x² = x*x

x³= x*x*x

etc…

and even with negative numbers you’re still multiplying the number by itself

like (x)-² = 1/x² = 1/(x*x)

In: 1797

Answer 1

I think there are many answers are so wrong here 🙂 I am a mathematician and if you search nesin math village on google you will see really good things 🙂 The power of a number is inductive relation that is why we have to make those definitions

2^(0) =1

and every number satisfying n>1

2^(n)=2 x 2^(n-1)

So we can define negative powers of a number so that

2^(-n) = (2^(n))^(-1) = 1/2^(n)

if you check these definitions there is no gape about any integer power of a number.

So this is explaining us why 2^(0)=1 is 🙂 it is just by definition.

(I am so sorry for mistakes my english is now very well 🙂