perplexus.info :: Just Math : Power

Power - ful (Posted on 2003-12-31)

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
answer	K Sengupta	2008-02-07 05:11:54
Solution	Praneeth	2007-07-26 12:02:24
just how big is it	Daniel	2006-07-03 02:13:36
re: Possible Solution	P C	2004-02-04 21:47:04
Possible Solution	Kerry Graham	2004-01-06 11:00:28
Solution	John Miller	2004-01-01 18:09:33
Solution	Dan Blume	2003-12-31 15:10:16
re:	Charlie	2003-12-31 10:58:39
No Subject	luminita	2003-12-31 10:41:34
solution	Charlie	2003-12-31 10:35:24
Almost (50%) there	Federico Kereki	2003-12-31 09:58:58

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