0^0
  (\be.eb)(\sz.z)(\sz.z)
      [b := (\sz.z)]
  (\e.e(\sz.z))(\sz.z)
      [e := (\sz.z)]
  ((\sz.z)(\sz.z))
      [s := (\sz.z)]
  ((\z.z))

Lambda Calculus returns (\z.z) AKA the Identity Function. Which kinda sounds like 1, except 1 is usually represented as (\sz.sz). Which means 0^0 is NaN? I wonder if division by zero also gives (\z.z), but I don't know what division in Lambda Calculus looks like.