What is the largest number among the following?
- (a) (1/2)^-6
- (b) (1/4)^-3
- (c) (1/3)^-4 ✓ UPSC's answer
- (d) (1/6)^-2
Why the answer is (c)
• To compare the numbers, convert each expression with a negative exponent into a positive power by inverting the base fraction.
• Option (a) (1/2)^-6 becomes 2^6, which equals 64.
• Option (b) (1/4)^-3 becomes 4^3, which equals 64.
• Option (c) (1/3)^-4 becomes 3^4, which equals 81.
• Option (d) (1/6)^-2 becomes 6^2, which equals 36.
• Comparing the calculated values (64, 64, 81, and 36), 81 is the largest number, so option (c) is the correct answer.
Why the other options are wrong
- (a) (1/2)^-6
- The value of (1/2)^-6 is 64, which is smaller than the value of option (c), which is 81.
- (b) (1/4)^-3
- The value of (1/4)^-3 is 64, which is smaller than the value of option (c), which is 81.
- (d) (1/6)^-2
- The value of (1/6)^-2 is 36, which is the smallest among all the given options.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2020, held on 4 October 2020. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.