Question

12. The digit in the unit's place of the number (28)^999+(12)^289-(21)^467​

Answer 1

If you keep multiplying the end digit with the end digit, you will find that the digits are repeating.

8 → 64 → 32 → 16 → 48

So 8 → 4 → 2 → 6 → ...

2 → 4 → 8 → 16 → 12

So 2 → 4 → 8 → 6 → ...

1 → 1 → ...

Clearly, the digits are repeating every 4 stages.

So let's divide each number by 4.

999 leaves remainder 3.

289 leaves remainder 1.

So, the unit's digit of each number is

2, 2, and 1

→ 2+2-1=3

So the answer is 3.