NCERT Solutions Class 9 Maths Chapter 1 Number Systems Ex 1.6

NCERT Solutions Class 9 Maths 
Chapter – 1 (Number Systems ) 

The NCERT Solutions in English Language for Class 9 Mathematics Chapter – 1 Number Systems Exercise 1.6 has been provided here to help the students in solving the questions from this exercise. 

Chapter 1: Number Systems

• NCERT Solution Class 9 Maths Ex – 1.1
• NCERT Solution Class 9 Maths Ex – 1.2
• NCERT Solution Class 9 Maths Ex – 1.3
• NCERT Solution Class 9 Maths Ex – 1.4
• NCERT Solution Class 9 Maths Ex – 1.5

Exercise – 1.6 

1. Find:
(i)
(ii)
(iii)

Answer –
(i)  

⇒ = (8 × 8)^1/2
⇒ (8²)^½
⇒ 8¹              [⸪ 2 × =1]
⇒ 8

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

(iii) 125^1/3
(125)^1/3 = (5×5×5)^1/3

⇒ (5³)^⅓
⇒ 5¹                    [⸪ 3 × = 1]
= 5

2. Find:
(i) 9^3/2
(ii) 32^2/5
(iii) 16^3/4
Answer –
(i) 9^3/2
9^3/2 = (3×3)^3/2
⇒ (3²)^3/2
⇒ 3³             [⸪ 2 × = 3]
⇒ 27

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

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

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

3. Simplify:
(i) 2^2/3 . 2^1/5
(ii)    

(iii)

(iv) 7^{1/2 .} 8^1/2

Answer –
(i) 2^2/3 . 2^1/5
⇒ 2^2/3 × 2^1/5
⇒ 2^{(2/3) + (1/5)}             [⸪ Since, a^m × aⁿ = a ^m+n]

⇒ 2^13/15                       [⸪ 2/3 + 1/5 = (2×5 + 3×1)/(3×5) = 13/15]

(ii)

⇒
⇒ (3^-3)⁷                     [⸪ Since, (a^m)ⁿ = a^{m x n}]
⇒ 3^-21

(iii)

⇒ = 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

⇒ 7^1/2 × 8^1/2
⇒ (7 × 8)^1/2                   [⸪ Since, (a^m × b^m = (a×b)^m]
= 56^1/2