198. 100^99 has 199 digits. Then we note that (100/99) ^ 99 is approximately 2.718 by approximation of e. As a result, 99^99 is approximately 100^99 / 2.718, which has 198 digits.
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Anonymous
Nov 13, 2014
(100-1)^99, with binomial theorem and a little bit analysis the answer can be obtained. 197 digits.