NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.6

Ex 1.6 Class 9 Maths Question 1.
Find:

Solution:
(i) 64 = 8 x 8 = 82
∴ (64)1/2 = (82)1/2 = 82 x 1/2 = 8 [(am)n = am x n]
(ii) 32 = 2 x 2x 2 x 2 x 2 = 25
∴ (32)1/5= (25)1/5= 25 x 1/5 = 2 [(am)n= am x n]
(iii) 125 = 5 x 5 x 5 = 53
∴ (125)1/3 = (53)1/3 = 53 x 1/3 = 5 [(am)n = am x n]

Ex 1.6 Class 9 Maths Question 2.
Find:

Solution:
(i) 9 = 3 x 3 = 32
∴ (9)3/2= (32)3/2 = 32 x 3/2 = 33 = 27
[(am)n = amn]
(ii) 32 = 2 x 2 x 2 x 2 x 2= 25
∴ (32)2/5 = (25)2/5 = 25 x 2/5 = 22 = 4
[(am)n = amn]
(iii) 16 = 2 x 2 x 2 x 2 = 24
∴ (16)3/4 = (24)3/4 = 24 x 3/4 = 23 = 8
[(am)n = amn]
(iv) 125 = 5 x 5 x 5 = 53
∴ (125)-1/3 = (53)-1/3 = 53 x (-1/3) = 5-1
= 15 [ a-n   1an ]

Ex 1.6 Class 9 Maths Question 3.
Simplify:

Solution:
(i) 22/3. 21/5 = 22/3 + 1/5 = 213/15
[am. an = am + n

(iv) 71/2.81/2 = (7 x 8)1/2 = (56)1/2 [am x bm = (ab)m]