How to calculate 9**(9**9) without spending a huge amount of time on it?

Question

Python

How can Python handle such large numbers when exponentiated? The final task is educational, it is necessary to return the last digit of the calculated number.

Answer 1

Algorithm:

1. pen write on paper the first few degrees 9
   
2. an idea pops up in my head
   

Answer 2

Even 2 digits:
(9+20(N-1))%100 - odd
abs(101-20N)%100 - even