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
Another way to think of this:
x^a * x^b = x^(a+b)
This is true for any positive values of a and b, so think about what x^0 needs to be to maintain this relationship.
if x^a * x^b = x^(a+b) , and b is zero, then you need
x^a * x^0 = x^(a+0) = x^a , which means x^0 must be 1.
You can then extrapolate that relationship with negative numbers as well.
Example, 2^5 is 32
2^5 * 2^-3 = 2 ^(5-3) = 2^2 = 4
So for this property to be consistent not just with positive exponents, but also negative exponents, this is the formulation we use.
To be clear, the notation of exponents is created by humans, but we want to create mathematical rules that are logical, consistent, and when feasible a useful description of reality.
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