Result of the $9^{9^9}$ So we were given a task for some bonus points to calculate and give the teacher the exact number of $9^{9^9}$. But the number is so big that I couldn't find where to calculate it to receive a precise number. I used python with a gmpy libraby to get a precise number but after almost 4 hours of running it crashed after it ran out of memory. So I am wondering is there actually a way to calculate the precise number?
 A: Since $9^9 = 387420489$, you have $$\log_{10} 9^{9^9} = 9^9 \log_{10} 9 = 369693099.6\ldots$$
so that the resulting number has 369,693,099 $+$ 1 digits.
A: First $~80$ digits:
$$428124773175747048036987115930563521339055482241443514174753723053523887471735048$$
The rest I can share with dropbox. My estimate - with mathematica it will take about $<7$ days to compute all digits, if you want to try run this:
res = 9^9^SetPrecision[9., M] 

where $M$  is the number of digits. First $10000$ digits take about $4$ minutes.
Update:
In Mathematica it take $9$ seconds. The trick to make it faster is to write
res = 9^(9^9);

that's what Robert Israel did in Maple
Update2:
Tried the same order of operations in Python - does not work
import gmpy2
a = gmpy2.mpz('9')**gmpy2.mpz('9')
gmpy2.mpz('9')**a

crashed kernel in 10 seconds. May be some memory issues.
A: Maple does
r := 9^(9^9):

in about 10 seconds on my computer.  Outputting the result to a file in Maple's internal format (an m-file) takes about 170 seconds (the file is about 208 Mb).   Saving to a text file (in decimal format) takes about 178 seconds: the file is about 379 Mb.
A: Well, whatever number you meant $x=(9^9)^9, 9^{9^9}$ you can give your teacher the answer:$x=1$. It is just written in the $x$-ary basis. 
It is impossible for any computer to calculate the second number $x$ in decimal expansion.
Edit: Clearly I was wrong regarding the computer power required to perform the calculation!
A: Let $y=9^{9^{9}}$
$\log_{10}(y) = 9^9\log_{10}(9) = 9^{9}\times \times 2 \times 0.4771  = 369676630.6038
$
So $\log_{10}(y) = 369676630.6038\Rightarrow y=10^{369676630.6038}$
