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You should take advantage of the fact that a^b == c^(Log[c,a] b) so that E^(E^(10^72)) == 10^(Log[10,E] E^(10^72)) == 10^(Log[10,E] 10^(Log[10,E] 10^72)) Since Log[10,E] (that is, ln(10)) is about 2.3, the number of digits in your quantity (in base 10) is ~ 2.3 10^(2.3*10^72)


10

I think you underestimate how many digits this number has. Even if you used scientific notation, the exponent would overflow your PC's memory, so you'd need scientific notation for the scientific notation. I'm not sure which number format you expect to get, but I think the form it's already in is probably the most useful. But let's try to get an idea for ...



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