The digit in the unit's place of 6^500 is:

The correct answer is Option (1) → 6

Only the units digits matter in a product. Since \(6 \times 6 = 36\) ends in 6, every power of 6 ends in 6:

    \(6^1 = 6, \quad 6^2 = 36, \quad 6^3 = 216, \quad 6^4 = 1296\)

In terms of modular arithmetic, \(6^2 \equiv 6 \pmod{10}\), so \(6^n \equiv 6 \pmod{10}\) for every n ≥ 1. So the units digit of \(6^{500}\) is 6.