The unit's place digit in (122)^173 is what and how?
Answers
The question is about the unit place of 122 raised to the power 173.
The unit place of 122 is 2.
The unit digits of powers of 2 are going in the following order:
2, 4, 8, 6.
Which means like,
2¹ ends in 2,
2² ends in 4,
2³ ends in 8,
2⁴ ends in 6,
2⁵ ends in 2,
2⁶ ends in 4,
2⁷ ends in 8,
2⁸ ends in 6,
and so on.
Thus the sequence is repeating.
So there are 4 possible numbers which comes in unit digits of the powers of 2.
Consider the exponent here, i.e., 173.
We have to divide this 173 by 4 and to find the remainder.
The remainder is 1.
As the remainder is 1, then the 1st term of the sequence 2, 4, 8, 6 is the answer.
If the remainder was 2, then the second term would be the answer.
If the remainder was 0, then the last term of the sequence would be.
Okay. The answer is 2, which is the first term of the sequence.
Plz ask me if you've any doubts.
Thank you. :-))