Think of the smallest number greater than 0...

[Værn]

Putting it to the negative infinity power will make it larger.

Don't think so.
10^3=1000
10^-3=.001
Multiplying by ten to a negative exponent makes the number smaller. Therefore...
10^-infinity=0.0000000000000000000000000000 0000000000000000000000000000000000000000 0000000000000000000000000000000000000000 0000000000000000000000000000000000000000 0000000000000000000000000000000000000000 0000000000000000000000000000000000000000 0000000000000000000000000000000000000000 0000000000000000000000000000000000000000 0000000000000000000000000000000000000000 0000000000000000000000000000000000000000 0000000000000000000000000000000000000000 0000000000000000000000000000000000000000 0000000000000000000000000000000000000000 000000000000000ooooooooooooooo..........
[Infinity is really big, I don't want to type the whole thing out. Skipping a bit.]
..........ooooooooooooooo0000000000000001