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

What others have written is correct, i am just presenting a different approach which uses limits:

So, just open the calculator app and use the power function with any number if you want,

Let’s take 2 in our example,

so (2)² = 4,
(2)¹ = 2

Keep decreasing the power

(2)⁰•⁹⁵ = 1.9318

(2)⁰•⁵ = 1.4142

(2)⁰•¹ = 1.0717

And so on…
So you can observe, in the equation (2)ˣ = y

As x tends to 0 ( X —-> 0)

We can see y tends to 1 ( y —-> 1)

Hence when x = 0, y should be 1