How do I use the quotient of powers property to show that zero to the zero power is undefined?
Think of x^n = (x^(n+1)) / x
so if x^1 =x, then x^0 = (x^1) / x = x / x =1
If x = 0 then: 0^1 = 0, so x ^ 0 = 0 / 0
now x / n heads towards (positive or negative) infinity as n becomes closer to 0.
As infinity is not a number, x / 0 has no numeric solution.