Argghh! Too many 5s
Number Theory
Level
2
Find the last three digits of: 5^(5^(5^ (5^5)))
The answer is 125.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Notice that as we raise 5 to odd numbers like 3, 5 or 7, the last three digits (units, tens and hundreds) are 125 while they are 625 for even numbers.
We know that 5^5 = 3125, which is odd. So all the subsequent exponents will be odd and the answer is 125.