-  Unit digit in (3127)173 - Unit digit in (7)173. Now, 74 gives unit digit 1
(7)173 = (74)43 x 71. Thus, (7)173 gives unit digit 7

To find the unit's digit in the product (3127)173, we need to determine the pattern of the unit's digit in the successive powers of 3127. The unit's digit of a number is the digit in the ones place, i.e., the rightmost digit of the number.

Let's consider the unit's digit of the first few powers of 3127:

3127^1 = 7

3127^2 = 9

3127^3 = 3

3127^4 = 1

3127^5 = 7

3127^6 = 9

3127^7 = 3

3127^8 = 1

We can see that the unit's digit repeats after every 4 powers of 3127. Therefore, we need to find the remainder when the exponent 173 is divided by 4.

173 ÷ 4 leaves a remainder of 1. This means that the unit's digit in (3127)173 will be the same as the unit's digit in (3127)1.

Thus, the unit's digit in the product (3127)173 is 7, which is the same as the unit's digit in the first power of 3127. Therefore, the correct answer is Option C, i.e., 7.

If you think the solution is wrong then please provide your own solution below in the comments section .