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)
• A negative power of a fraction inverts it: (1/k)⁻ⁿ = kⁿ.
• (a) 2⁶ = 64; (b) 4³ = 64; (c) 3⁴ = 81; (d) 6² = 36.
• The largest is 81.
• Hence option (c).
Why the other options are wrong
- (a) (1/2)⁻⁶
- (1/2)⁻⁶ = 2⁶ = 64, which is less than 81.
- (b) (1/4)⁻³
- (1/4)⁻³ = 4³ = 64, which is less than 81.
- (d) (1/6)⁻²
- (1/6)⁻² = 6² = 36, the smallest of the four.
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.