What is the Remainder of (32^31^301) when it is Divided by 9?

June 23, 2019

What is the Remainder of (32^31^301) when it is Divided by 9?

32^31^301
when 31 divided by 9 gives remainder 5
5 5^2 5^3 all gives the same unit digit 5
so 31^32 gives unit digit 5
same rule applicable to 31^301
when 31 divided by 9 gives remainder 4
4 4^2 4^3 4^4 =4 6 4 6 unit place repeats for every 2 times i,e for even power its uint place is 6 and for odd its 4
as 301 is odd its unit place is 4
so 31^32^301=31^4=5^4=5 is the ans