CTET Paper II (Mathematics and Science) 29 Jan 2023 Solved Paper

Concept:A negative fraction raised to an odd power remains negative, while a positive exponent in the denominator flips sign.Explanation:Check each option step by step.Option A: $(\frac{-1}{3})^{5} = \frac{(-1)^{5}}{3^{5}} = \frac{-1}{243}$ — matches the given value.Option B: $(\frac{1}{3})^{5} = \frac{1}{243}$, which is positive — not equal.Option C: $(\frac{1}{3})^{-5} = 3^{5} = 243$ — positive and too large.Option D: $(3)^{5} = 243$ — also positive and too large.Only Option A gives the required negative fraction.Answer:A. $(\frac{-1}{3})^{5}$