Main Application? To find the last digit of a power expression
The last digit of a number of the form ab falls in a particular sequence or order depending on the unit digit of the number
(a) and the power the number is raised to
(b). The power cycle of a number thus depends on its’ unit digit.
Consider the power cycle of 2
23=8 27 =128
24=16 28 =256
As it can be observed, the unit digit gets repeated after every 4th power of 2. Hence, we can say that 2 has a power cycle of 2,4,8,6 with frequency 4.
This means that, a number of the form
24k+1 will have the last digit as 2
24k+2 will have the last digit as 4
24k+3 will have the last digit as 8
24k+4 will have the last digit as 6 (where k=0, 1, 2, 3…)
This is applicable not only for 2, but for all numbers ending in 2. ( eg 1232 ,3452123)
Therefore to find the last digit of a number raised to any power, we just need to know the power cycle of digits from 0 to 9, which is given below
|Unit digit||Power cycle||Frequency|
Note:- You don’t need to remember the frequencies, as in every case, the frequency of 4 is valid.