Last digit/unit place Lesson 2

In the previous lesson, the sum was easy nut to crack. Now i am coming to the original beauty of the CAT by following sum.
Question: Wht is the unit digit of

A^B

Ans: Follow the following Algorithm:
Divide the B by4. Get the remainder (say) r.Obviously r=0,1,2,3. (i.e. o≤r<4)
I am taking 2 cases:-
Case 1: 0< r<4 r="1,2,3
Then the original sum reduces to

A^r

which one can find easily.

Example: What is the unit digit of

3^26021983

Divide 26021983 by 4. Remainder is 3. So, the sum becomes

3³

and the ans. is 27 i.e. 7. .............Continued in next lesson..........