1/ infinity is 0, and 0^0 is either undefined or 1, depending on context.
More *diots.
(1/infinity)^-1=infinity while (-1/infinity)^-1 =-infinity
Showing they differ, for if they did not they would both equal 0.
And if x is s 0 then x^x=x/x will equal 0^0/0/0 just the as infinity^infinity will equal infinity/infinity
It is the number that must be raised to the power of ♾️ , to equal 1/♾️ which is any number greater than 0, but less than 1.
Whereas, the ratio (0^0) shall equal any number of any range.