NCERT Solutions Class 9th Maths Chapter – 1 Number System Exercise – 1.5

Question 1. Find:

(i) 64^1/2

Solution – 64^1/2
= (8×8)^1/2
= (8²)^½
= 8¹ [⸪2×1/2 = 2/2 =1]
= 8

(ii) 32^1/5

Solution – 32^1/5
= (2⁵)^1/5
= (2⁵)^⅕
= 2¹ [⸪5×1/5 = 1]
= 2

(iii) 125^1/3

Solution – (125)^1/3
= (5×5×5)^1/3
= (5³)^⅓
= 5¹ (3×1/3 = 3/3 = 1)
= 5

Question 2. Find:

(i) 9^3/2

Solution – 9^3/2
= (3×3)^3/2
= (3²)^3/2
= 3³ [⸪2×3/2 = 3]
=27

(ii) 32^2/5

Solution – 32^2/5
= (2×2×2×2×2)^2/5
= (2⁵)^2⁄5
= 2² [⸪5×2/5= 2]
= 4

(iii)16^3/4

Solution – 16^3/4
= (2×2×2×2)^3/4
= (2⁴)^3⁄4
= 2³ [⸪4×3/4 = 3]
= 8

(iv) 125^-1/3

Solution – 125^-1/3
= (5×5×5)^-1/3
= (5³)^-1⁄3
= 5^-1 [⸪3×-1/3 = -1]
= 1/5

(i) 2^2/3 . 2^1/5

Solution – 2^2/3×2^1/5
= 2^(2/3)+(1/5) [⸪Since, a^m × aⁿ=a ^{m + n} ____ Laws of exponents]
= 2^13/15 [⸪2/3 + 1/5 = (2×5+3×1)/(3×5) = 13/15]

(ii) (1/3³)⁷

Solution – (1/3³)⁷
= (3^-3)⁷ [⸪Since,(a^m)ⁿ = a^{m x n}____ Laws of exponents]
= 3^-21

(iii) 11^1/2/11^1/4

Solution – 11^1/2/11^1/4
= 11^(1/2)-(1/4)
= 11^1/4 [⸪(1/2) – (1/4) = (1×4-2×1)/(2×4) = 4-2)/8 = 2/8 = ¼ ]

(iv) 7^1/2×8^1/2

Solution – 7^1/2×8^1/2
= (7×8)^1/2 [⸪Since, (a^m × b^m = (a × b)^m ____ Laws of exponents]
= 56^1/2