The unit's digit of 2^2025 is

The correct answer is Option (2) → 2

The unit digits of the powers of 2 repeat in a cycle of length 4:

    \(2^1 = 2,\; 2^2 = 4,\; 2^3 = 8,\; 2^4 = 16,\; 2^5 = 32, \ldots\)

so the unit digits run 2, 4, 8, 6, 2, 4, … Dividing the power by 4:

    \(2025 = 4 \times 506 + 1\)

The remainder 1 gives the first digit of the cycle, so the unit digit of \(2^{2025}\) is the same as that of \(2^1\), which is 2.