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'.]

the last digit is 6.

the last digits of the 8 powers' are: 8, 4, 2, 6 and so on. the final power is 7! = 5040
5040 = 4 (mod 4) which means that 5040 is divisible by 4,
so the last digit of the 8^5040 is the same as the last digit of 8^4, that is 6

Posted by luminita on 2003-12-31 10:41:34