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What is the units digit of 167¹³¹?
- 7
- 9
- 1
- 3
Correct answer: 3
Solution
The units digit of 167¹³¹ equals the units digit of 7¹³¹. The cycle of units digits for powers of 7 is: 7¹=7, 7²=49 (units 9), 7³=343 (units 3), 7⁴=2401 (units 1), then it repeats with period 4. 131 = 4*32 + 3, so 7¹³¹ has the same units digit as 7³ = 3.
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