What is the last digit of the number:

8^(7^(6^(5^(4^(3^(2^1))))))

[(a)^b implies 'a' raised to the power of 'b', ((a)^b)^c implies 'a' raised to the power 'bc', but a^(b^c) implies 'a' raised to the power 'b' raised to the power 'c'.]

There is a 6 raised to a power. The result of that power must be even, as six is even.

7, raised to an even power, always results in a number that is congruent to 1 mod 4.

When 8 is raised to a power that is congruent to 1 mod 4, the last digit is 8.

Posted by Charlie on 2003-12-31 10:35:24