Why does any value or variable raised to a power of zero equal one?

Answer 1

Say you were given a piece of paper and began to cut it up:-

0 cuts 1 piece or 20

1 cut gives 2 pieces or 21

2 cuts gives 4 pieces or 22

3 cuts gives 8 pieces or 23

4 cuts gives 16 pieces or 24

and so on ......

Answer 2

It seems to be primarily for mathematical convenience, as opposed to any other reason. (The same reason that 0! (factorial) equals one. This prevents many sums leading to a "something divided by zero" answer, which clearly is not a feasible answer.) Many things are "invented" just for mathematical convenience, such as the imaginary number "i" - although it does not technically exist, it aids mathematical completeness - i.e the ability to solve problems.

Additional Information:-

Let any number or variable be n:

So n2/n2 = 1 because when dividing indices with the same bases we subtract the indices and n2 divided by n2 is the same as n2-2 which is n0 and is equal to 1