metadata
source: ncert_exercises
topic: numbers
class_level: class_9
chapter: ch1
exercise: ex1.6
difficulty: intermediate
Class 9 | Ch1: Number Systems | Exercise 1.6
Q1. Find: (i) 64^(1/2) (ii) 32^(1/5) (iii) 125^(1/3) Answer: (i) √64=8. (ii) (2⁵)^(1/5)=2. (iii) (5³)^(1/3)=5. ✅ Rule: a^(1/n) = nth root of a.
Q2. Find: (i) 9^(3/2) (ii) 32^(2/5) (iii) 16^(3/4) (iv) 125^(-1/3) Answer: (i) (√9)³=3³=27. (ii) (32^(1/5))²=2²=4. (iii) (16^(1/4))³=2³=8. (iv) 1/(125^(1/3))=1/5. ✅ Rule: a^(m/n)=(a^(1/n))^m.
Q3. Simplify: (i) 2^(2/3)×2^(1/5) (ii) (1/3³)^7 (iii) 11^(1/2)/11^(1/4) (iv) 7^(1/2)×8^(1/2) Answer: (i) 2^(13/15). ← aᵐ×aⁿ=aᵐ⁺ⁿ, 2/3+1/5=13/15. (ii) 3^(-21). ← (aᵐ)ⁿ=aᵐⁿ. (iii) 11^(1/4). ← aᵐ/aⁿ=aᵐ⁻ⁿ, 1/2-1/4=1/4. (iv) (7×8)^(1/2)=56^(1/2)=2√14. ✅