NCERT Solutions Class 9 – Chapter 1 Number System – Exercise 1.5 (original) (raw)

Last Updated : 25 Apr, 2024

**Question 1. Find the Value of:

****(i) 64** 1/2

641/2

= (8 × 8)1/2

= (82)½

= 81

= 8

****(ii) 32** 1/5

321/5

= (2 x 2 x 2 x 2 x 2)1/5

= (25)⅕

= 21

= 2

****(iii) 125** 1/3

(125)1/3

= (5 × 5 × 5)1/3

= (53)⅓

= 51

= 5

**Question 2. Find the value of:

****(i) 9** 3/2

93/2

= (3 × 3)3/2

= (32)3/2

= 33

= 27

****(ii) 32** 2/5

322/5

= (2 × 2 × 2 × 2 × 2)2/5

= (25)2⁄5

= 22

= 4

****(iii) 16** 3/4

163/4

= (2 × 2 × 2 × 2)3/4

= (24)3⁄4

= 23

= 8

****(iv) 125** -1/3

125-1/3

= (5 × 5 × 5)-1/3

= (53)-1⁄3

= 5-1

= 1/5

**Question 3. Simplify the followings:

****(i) 2** 2/3 × 2 1/5

22/3 × 21/5

= 2(2/3) + (1/5) ⸪ As, a m **× a n **= a m + n

= 213/15

****(ii) (1/3** 3 ) 7

(1/33)7

= (3-3)7 ⸪ As, ****(a** m ) n = a m x n

= 3-21

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

111/2/111/4

= 11(1/2) - (1/4) ⸪ As, **a m × a -n = a m - n

= 111/4

****(iv) 7** 1/2 **× 8 1/2

71/2 × 81/2

= (7 × 8)1/2 ⸪ As, **a m × b m = (a × b) m

= 561/2