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Unit digit of the multiplication of 21531672153^{167}2153167​ is 
Question

Unit digit of the multiplication of 21531672153^{167}​ is 

A.

1

B.

7

C.

3

D.

9

Correct option is B

Given:
Find the unit digit of  (2153)167(2153)^{167}​​
Formula used:
If the unit digit of base is  a, then unit digit of  ana^n ​ follows a repeating cycle.
Solution:
Unit digit of  2153  is 3 
Powers of 3 have the following unit digit cycle:
31=332=933=27=>unit digit 734=81=>unit digit 1Cycle: (3,9,7,1), length = 43^1 = 3 \\3^2 = 9 \\3^3 = 27 \Rightarrow \text{unit digit } 7 \\3^4 = 81 \Rightarrow \text{unit digit } 1 \\\text{Cycle: } (3, 9, 7, 1), \text{ length = 4} \\​​
Find 167 mod 4=3\mod 4 = 3 \\​​
So, the unit digit of 3167 3^{167} is the 3rd digit in the cycle - 7
Correct answer is (b).

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