Finding the Unit digit

Here's how i'd approach this problem.

264^102[ 264+1] - factorize

264^102 (265)

Now since the question is about units digit we care about multiplication in only in units digit.

Units digit in 264 -4 ; take the square of 264 - 4*4=16; 6 in units digit ( coz we care only about multiplication in units digit- 4*4=16, in which units digit is 6).

next take 264^3 - gives 4*4*4= 6(from 4*4) *4 = 4 in units digit;

264^4 - 4 in units digit again.

See the pattern; we get 4 in units place when power is odd and 6 in units place when power is even.

Since 102 is even, 264^102 has 6 in units place.

Now muliply 6*5 (units digit from 265)=30 or 0 in units digit.

What is the OA?

Thanks Rahul, this means that i can apply this method of even power and odd power applicable to only 9 because it has also got a cyclicity of 2?

How about other numbers such as 2, 3, 5?

Can you provide some more similar questions or probably a link on this topic for practice?

gdk800 wrote:Pls help with the following problem.

Unit digit of (264)^103 + (264)^102 = ?

I would like to do some change, (264)^103 + (263)^102
What should be the answer now,