Question
The unit digit in the expansion of $(2137)^754$ is
Answer: Option A
Answer: (a)Expression = $(2137)^754$ Unit’s digit in 2137 = 7 Now, $7^1 = 7, 7^2 = 49, 7^3 = 343, 7^4 = 2401, 7^5$ = 16807, ... Clearly, after index 4, the unit’s digit follow the same order. Dividing index 754 by 4 we get remainder = 2∴ Unit’s digit in the expansion of $(2137)^754$ = Unit’s digit in the expansion of $(2137)^2$ = 9
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Answer: (a)Expression = $(2137)^754$ Unit’s digit in 2137 = 7 Now, $7^1 = 7, 7^2 = 49, 7^3 = 343, 7^4 = 2401, 7^5$ = 16807, ... Clearly, after index 4, the unit’s digit follow the same order. Dividing index 754 by 4 we get remainder = 2∴ Unit’s digit in the expansion of $(2137)^754$ = Unit’s digit in the expansion of $(2137)^2$ = 9
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