In order to understand why everything to the zeroth power equal one, let's do some examples.
8^0
= 8^(1-1)
= (8^1)(8^-1)
= (8)(1/8)
= 8/8
= 1
2^0
= 2^(2-2)
= (2^2)(2^-2)
= (4)(1/2^2)
= (4)(1/4)
= 4/4
= 1
(x + 1)^0
= (x + 1)^(1-1)
= [(x + 1)^1][(x + 1)^-1]
= (x+ 1)[1/(x + 1)]
= (x + 1)/(x + 1)
= 1
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Anything to the zeroth power is one. It doesn't matter what x is. 2 to the zeroth power is one.
I don't like this answer, but according to mathematical theory, anything but zero ,to the zeroth power is set equal to "one".
When we raise a number to the zeroth power, that means we multiply the number by itself zero times. So, the reason that any number to the zero power is one is because any number to the zero power is just the product of no numbers at all, which is the multiplicative identity, 1.
Zero to the zeroth power is commonly held to be one (1) by several definitions and ways of determining it. Some uses may define it as zero as well, or as another number or undefined.
2 to the power of negative one is equal to 0.5