NCERT Solutions Class 9 Mathematics Number System Exercise 1.6

Exercise 1.6

Question : 1:Find:             (i) 64^1/2                           (ii) 32^1/5                            (iii) 125^1/3               

Answer :

(i) 64^1/2 = (8²)^1/2 = 8^{2 * 1/2} = 8¹ = 8                          

(ii) 32^1/5 = (2⁵)^1/5 = 2^{5 * 1/5} = 2¹ = 2                           

(iii) 125^1/3 = (5³)^1/3 = 5^{3 * 1/3} = 5¹ = 5

Question : 2:Find:         (i) 9^3/2                    (ii) 32^2/5                          (iii) 16^3/4                         (iv) 125^-1/3               

Answer :

(i) 9^3/2 = (3²)^3/2 = 3^{2 * 3/2} = 3³ = 27                                           

(ii) 32^2/5 = (2⁵)^2/5 = 2^{5 * 2/5} = 2² = 4                                                      

(iii) 16^3/4 = (2⁴)^3/4 = 2^{4 * 3/4} = 2³ = 8                                                           

(iv) 125^-1/3 = (5³)^-1/3 = 5^{3 * (-1/3)} = 5^-1 = 1/5