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What is the number in the unit place of the number (129)58?
- a)1
- b)2
- c)4
- d)9
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
What is the number in the unit place of the number (129)58?a)1b)2c)4d)...
To determine the units digit of 12958129^{58}, focus on the units digit of the base, which is 9. The pattern of units digits for powers of 9 is as follows:
- 91=9 (units digit: 9)
- 92=81 (units digit: 1)
- 93=729 (units digit: 9)
- 94=6561 (units digit: 1)
The pattern (9, 1) repeats every two powers.
Since 58 is even, it corresponds to 92, where the units digit is 1.
Thus, the units digit of 12958 is 1.
Most Upvoted Answer
What is the number in the unit place of the number (129)58?a)1b)2c)4d)...
Understanding the Problem
To find the unit place of the number (129)^58, we need to focus on the last digit of the base number, which is 9. The last digit of a number raised to a power determines the unit place of the result.
Last Digit Pattern of 9
When raising 9 to any power, a pattern emerges in the unit digits:
- 9^1 = 9 (last digit is 9)
- 9^2 = 81 (last digit is 1)
- 9^3 = 729 (last digit is 9)
- 9^4 = 6561 (last digit is 1)
From this, we can see that:
Analyzing the Exponent
In our case, we have 9 raised to the power of 58, which is an even number. According to the pattern established:
Conclusion
Thus, the unit place of the number (129)^58 is 1. The correct answer is option 'A'.
To find the unit place of the number (129)^58, we need to focus on the last digit of the base number, which is 9. The last digit of a number raised to a power determines the unit place of the result.
Last Digit Pattern of 9
When raising 9 to any power, a pattern emerges in the unit digits:
- 9^1 = 9 (last digit is 9)
- 9^2 = 81 (last digit is 1)
- 9^3 = 729 (last digit is 9)
- 9^4 = 6561 (last digit is 1)
From this, we can see that:
- The last digit of 9 raised to an odd power (like 1, 3, etc.) is 9.
- The last digit of 9 raised to an even power (like 2, 4, etc.) is 1.
Analyzing the Exponent
In our case, we have 9 raised to the power of 58, which is an even number. According to the pattern established:
- Since 58 is even, the last digit of (129)^58 or 9^58 will be 1.
Conclusion
Thus, the unit place of the number (129)^58 is 1. The correct answer is option 'A'.
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What is the number in the unit place of the number (129)58?a)1b)2c)4d)9e)None of theseCorrect answer is option 'A'. Can you explain this answer? for SSC CGL 2025 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about What is the number in the unit place of the number (129)58?a)1b)2c)4d)9e)None of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for SSC CGL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the number in the unit place of the number (129)58?a)1b)2c)4d)9e)None of theseCorrect answer is option 'A'. Can you explain this answer?.
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