Question

The difference between the last two digits of the numbers
(78)^379 and (54)^380​

Answer 1

Answer:

Step-by-step explanation:

78^379 can be simplified as:

78^379 = (2 × 39)^379

=> 2^379 × 39^379

=>(2^10)37 × 2^9 × (39^2)^189 × 39

here, 2^10 ends in 4, 2^9 end in 2, 39^2 ends in 1 and 39 ends in 9

=> 4 × 2 × 1 × 9 = 2 (the unit digit of 78^379)

in 54^380, cyclicity of 4 is 2, which means every alternate power the unit digit will be 4 and every second power the unit digit will be 6

since 380 is divisible by 2, the unit digit of 54^380 is 6

6-2= 4, which is the answer