The digit in the unit place of the number $6^{129}$ x $7^{307}$ is

Correct Answer: (C) 8

For any positive integer power, $6^{129}$ always has a units digit of 6. For powers of 7, the units digits cycle every 4 powers: $7^1 \to 7$, $7^2 \to 9$, $7^3 \to 3$, $7^4 \to 1$. Evaluating the exponent modulo 4: $307$$\equiv$ 3 \pmod 4, so $7^{307}$ has a units digit of $7^3 \to 3$. Multiplying the units digits gives $6$$\times$ 3 = 18, which ends in 8. Thus, the units digit of the product is 8.