What is the unit digit of the exponential integer 7^95?
Answer and explanation
Correct answer: D. 3
- Step 1: Unit digits of powers of 7 cycle in periods of 4: 7^1 = 7, 7^2 = 9, 7^3 = 3, 7^4 = 1. Step 2. Evaluate exponent modulo 4: 95 = 4 23 + 3. The remainder 3 corresponds to the third term in the cycle, which is 3. Answer: 3. Why not the others:* 7 corresponds to remainder 1; 9 corresponds to remainder 2; 1 corresponds to remainder 0.
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