What is the units digit of 3²¹?
Answer and explanation
Correct answer: C. 3
- Step 1: The units digits of the powers of 3 repeat in a cycle of four: 3, 9, 7, 1. Step 2. 21 = 5 × 4 + 1, so 3²¹ is at the first position of the cycle: 3. Answer: 3. Why not the others: 9: This is the units digit of 3² and 3⁶, where the cycle is at the second position. 7: This is the units digit of 3³, where the cycle is at the third position. 1: This is the units digit of 3⁴, at the end of a cycle.
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