Why is a to the power 0 equal to 1?

Answer 1

It's difficult to describe and i don't think there is an answer but it is a fact which must be memorized. It would be the number to the power of nothing so 5 times 0 is well 5 but it just is one!

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Can't see any links, but here is an answer:

Any number to the power zero is equal to one. That can be derived from the following index law:

xa*xb = xa+b (x not zero)

Now let b = 0 so that the above becomes

xa*x0 = xa+0

so

xa*x0 = xa (since a+0 = a)

That is, any number multiplied by x0 is the number itself. That can be true only if x0 is the multiplicative identity, that is, only if x0 = 1.