If 9^9^9 is written out in the usual manner, how many digits will be needed?
Assume that your question is (9^9)^9 which is equal to 9^81. Using Maple, we can get
which includes 78 digits.
But if your question is 9^(9^9)=9^387420489, then the answer is not clear. I try to get it by using Maple ...
How many digits will it take to represent 9^9^9 power?