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Power - ful (Posted on 2003-12-31) Difficulty: 3 of 5
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'.]

  Submitted by Ravi Raja    
Rating: 3.4000 (5 votes)
Solution: (Hide)
We leave out all the numbers and start with 6. Now, we know that whenever 6 is raised to any power, the result is always even, since 2 is a factor of 6. Next, we see that, when 7 is raised to an even power, it always results in a number that is congruent to 1 mod 4, and finally, when 8 is raised to a power that is congruent to 1 mod 4, the last digit is 8.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
answerK Sengupta2008-02-07 05:11:54
SolutionSolutionPraneeth2007-07-26 12:02:24
just how big is itDaniel2006-07-03 02:13:36
re: Possible SolutionP C2004-02-04 21:47:04
Possible SolutionKerry Graham2004-01-06 11:00:28
SolutionJohn Miller2004-01-01 18:09:33
SolutionSolutionDan Blume2003-12-31 15:10:16
re:Charlie2003-12-31 10:58:39
SolutionNo Subjectluminita2003-12-31 10:41:34
SolutionsolutionCharlie2003-12-31 10:35:24
Some ThoughtsAlmost (50%) thereFederico Kereki2003-12-31 09:58:58
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