Question

What is the units digit of \(7^{95}\)?

• A. 7
• B. 9
• C. 1
• D. 3

Hint:

Units digits of powers of 7 repeat in a cycle of length 4.

Answer 1

The Correct Option is D

Step 1: Find the cycle of units digits of powers of 7.
\(7^1 = 7\), \(7^2 = 49\) (ends 9), \(7^3 = 343\) (ends 3), \(7^4 = 2401\) (ends 1). The cycle 7, 9, 3, 1 has length 4.
Step 2: Reduce the exponent modulo 4.
\(95 = 4 \times 23 + 3\), so the units digit matches the 3rd term of the cycle.
Step 3: Read off.
The 3rd term is \(3\). Units digit \(= \boxed{3}\).