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
Both can happen, it depends on what kind of thing is x and in what context. Sometimes x^0 =1 and sometimes x^0 is undefined.
There are some context where x^0 doesn’t “make sense”, and in that case it might be better to leave x^0 undefined.
But when it does make sense, why not define it? The more possible input the operation can accept, the more manipulation you can do. There are generally no harm in defining the operation to work on extra input. The only possible downside is that if the extra input is useful, then it’s not worth the effort of defining it.
When x is a number (in many sense of “number”) and 0 is supposed to be a natural number 0 or an integer 0, then x^0 =1. Why? Think about sum. If x*0 is x add to itself 0 times, and you know x*0 =0, right? To perform a sum, you start with 0, and keep adding, so if there are nothing to add, you get 0 back. Same here. x^0 mean x times itself 0. To perform a product, you start with 1, and keep multiplying. If you have nothing to multiply, you get back 1.
This convention is called “empty product equal 1” convention. This is applicable to all forms of product. If someone say “what’s the product of all prime numbers strictly less than n” and n happen to be 2, then the answer is 1, because there are no prime numbers strictly less than 2.
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