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?
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.
Let $y=9^{9^{9}}$

$\log_{10}(y) = 9^9\log_{10}(9) = 9^{9}\times \times 2 \times 0.4771  = 369676630.6038
$

So $\log_{10}(y) = 369676630.6038\Rightarrow y=10^{369676630.6038}$