Why any number having the power of zero is equal to one

SOLUTION

Any number to the zero power always gives one.

One rule for exponents is that exponents add when you have the same base. So if you have a number, x, and exponents, a and b, then:
x^a * x^b = x^(a+b)
So then if we make one of the exponents negative:x^a * x^-b = x^(a-b)
And if the exponents are the same magnitude (a = b)x^a * x^-b = x^a * x^-a = x^(a-a) = x⁰

Now, remember that if you have a negative exponent, it means you have one divided by the number to the exponent:

x^-a = 1/x^a
So, we can also write x^a * x^-a in a different way:
x^a * x^-a = x^a * 1/x^a = x^a/x^a
And a number divided by itself is always 1 so:
x^a * x^-a = x^a* 1/x^a = x^a/x^a = 1:
So now we've shown that:
x^a * x^-a = x^(a-a) = x⁰
and
x^a * x^-a = x^a * 1/x^a:
This means that any number x⁰ = 1.