The digit in the unit place of the number $6^{129} \times 7^{307}$ is
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Correct Answer: Option C
Detailed Explanation:
Unit digit of 6^129: Any power of 6 always ends in 6 (since 6×6=36, 36×6=216, etc.). Thus, unit digit = 6.
Unit digit of 7^307: Powers of 7 cycle every 4: 7¹→7, 7²→9, 7³→3, 7⁴→1. Divide 307 by 4: remainder = 3. So unit digit matches 7³ = 3.
Final unit digit: Multiply 6 × 3 = 18, giving unit digit 8.
Therefore, the unit digit is 8, making Option 3 the correct answer.
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