Find the unit digit of \(7^{105}\).
Answer: C
The power cycle of the unit digit for 7 is (7, 9, 3, 1), with a length of 4. We find the remainder of the power \(105\) when divided by 4. \(105 \div 4\) gives a remainder of 1. The required unit digit is the 1st in the cycle, which is 7.