What is the unit digit in 189^723? A] 7 B] 9 C] 1 D] 3 Options : A B C D
Question
What is the unit digit in 189^723?
A] 7
B] 9
C] 1
D] 3
Options :
A
B
C
D
Solution
1. Break Down the Problem
To find the unit digit of , we only need to consider the unit digit of the base number, which is in this case. Therefore, we will find the unit digit of .
2. Relevant Concepts
The unit digits of the powers of follow a pattern:
- has a unit digit of
- has a unit digit of
- The pattern repeats every two powers:
3. Analysis and Detail
To determine the unit digit of , we find the exponent modulo : Since is odd, the unit digit corresponds to the first element in the pattern which is .
4. Verify and Summarize
Through our analysis, we see that the unit digit of is . Since is odd, also has a unit digit of .
Final Answer
The unit digit in is 9 (Option B).
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