Unit digit of exponential expression

The unit digit depends entirely on the base unit 2 and the behavior of its exponent modulo 4. The cyclicity of 2 is 4, repeating the pattern {2, 4, 8, 6}.

Evaluate the exponent E = 9 × 7 × 5 × 3 × 1 modulo 4. Convert each individual factor into its remainder format modulo 4: 9 \equiv 1 ± od 4 7 \equiv 3 ± od 4 5 \equiv 1 ± od 4 3 \equiv 3 ± od 4 1 \equiv 1 ± od 4

Multiply the remainders together: 1 × 3 × 1 × 3 × 1 = 9. 9 ± od 4 = 1. Since the net remainder is 1, the unit digit matches the first step of the cyclicity loop, which is 2^1 = 2.

Answer: (a).