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

Let’s look at powers of 2:

2¹=2
2²=4
2³=8
2⁴=16
2⁵=32

So to get the next power of 2, you just multiply by 2 (2×2=4, 4×2=8, 8×2=16, …). Which means to get the previous power, you need to *divide* by 2. So 2⁰ should be 2¹/2=2/2=1.