Question

Find the unit digit of (14)^124*(29)123 using modulus.

Answer 1

14^124 ×29^123 will have last digit same as that of last digit of 
4^124 × 9^123
Now we know that 9 to the power odd number will end with 9 and to the even power will end with 1.
So here , 9^123 will end with 9.
For 4^124 = (4^2)^62 =  16^62 and we know that if the last digit is 6 then it will always end with 6 for any power of 6.
So last digit of 4^124 is 6
Now last digit of 14^124 ×29^123 = 6 × 9 = 54


So last or unit digit is 4