Can someone please explain this problem.

Module 5 Day 3 Your Turn Part 3 MiniQuestion Solution
It says that this number is odd, when it is even because 8^7^6^5 and so on can be expressed as 8^(7!), and we know that even*even=even.

Very close! It would only be equal to 8^(7!) if there were parentheses around each term like this:
If there are no parentheses, the powers cannot be multiplied, and so it equals this:
Since the exponent on the 8 is a power of 7, which is odd, the answer is equal to 8^{1} mod 9. 
@v4913 said in Can someone please explain this problem.:
Very close! It would only be equal to 8^(7!) if there were parentheses around each term like this:
If there are no parentheses, the powers cannot be multiplied, and so it equals this:
Since the exponent on the 8 is a power of 7, which is odd, the answer is equal to 8^{1} mod 9.o pro v4913 post o

@v4913 Ok, thanks! I also have another question about this problem. When it is odd, why is the answer 1 mod 9?

@neatlobster @v4913 Thank you

This post is deleted! 
@neatlobster Good question! Since 8 = 1 mod 9, and the powers of 1 go 1, 1, 1, 1, etc, all (1)^{even} = 1 mod 9 and all (1)^{odd} = 1 mod 9. Since we are talking about modulos, and 8 is the same as 1 mod 9, this means (8)^{even} = 1 mod 9, and (8)^{odd} = 1 mod 9.