To find the last digit of an expression which is in the format of ab
Cyclicity of unit digit of an expression:
From the table it is clearly visible that for all the numbers whose unit digit in the format of 2b, the unit digits are respectively 21 = 2, 22 = 4, 23 = 8, 24 = 6, 25 = 2
Similarly we can find unit digits for the remaining numbers easily.
Please observe, The cyclicity of the numbers 2, 3, 7, 8 is 4, and for 4, 9 is 2 as the pattern is repeating after power 4. The cyclicity of 0, 1, 5, 6 is 1.
What is the unit digit of the expression 317171
Here we can concentrate only on the unit digit of the base and the power. Unit digit of the base is 7 so from the table its cyclicity is 4.
Let us find the remainder when 171 is divided by 4. For the divisibility rule for the 4 is to find the remainder of the last two digits of 171, so 71 when divided by 4 gives a remainder 3. So from the table unit digit of 73 is 3.