# Bihar Board Class 9 Maths Solutions Chapter 1 संख्या पद्धति Ex 1.6

Bihar Board Class 9 Maths Solutions Chapter 1 संख्या पद्धति Ex 1.6 Text Book Questions and Answers.

## BSEB Bihar Board Class 9 Maths Solutions Chapter 1 संख्या पद्धति Ex 1.6

प्रश्न 1.
ज्ञात कीजिए
(i) 64$$\frac{1}{2}$$
(ii) 32$$\frac{1}{5}$$
(iii) 125$$\frac{1}{3}$$
हाल:
(i) (64)$$\frac{1}{2}$$ = (8 × 8)$$\frac{1}{2}$$
= (8²)$$\frac{1}{2}$$ [∵ (xa)b = xab]
= 8

(ii) 32$$\frac{1}{5}$$ = (2 × 2 × 2 × 2 × 2)$$\frac{1}{5}$$
= (25)$$\frac{1}{5}$$
= 25×$$\frac{1}{5}$$ [∵ (xa)b = xab]
= 2

(iii) 125$$\frac{1}{3}$$ = (5 × 5 × 5)$$\frac{1}{3}$$
= (53)$$\frac{1}{3}$$
= 53×$$\frac{1}{3}$$ [∵ (xa)b = xab]
= 5

प्रश्न 2.
ज्ञात कीजिए
(i) 9$$\frac{3}{2}$$
(ii) 32$$\frac{2}{5}$$
(iii) 16$$\frac{3}{4}$$
(iv) 125$$\frac{-1}{3}$$
हल:
(i) 9$$\frac{3}{2}$$ = (3 × 3)$$\frac{3}{2}$$
= (32)$$\frac{3}{2}$$
= 32×$$\frac{3}{2}$$ [∵ (xa)b = xab]
= 3³
= 27

(ii) 32$$\frac{2}{5}$$ = (2 × 2 × 2 × 2 × 2)$$\frac{2}{5}$$
= (25)$$\frac{2}{5}$$
= 25×$$\frac{2}{5}$$ [∵ (xa)b = xab]
= 2²
= 4

(iii) 16$$\frac{3}{4}$$ = (2 × 2 × 2 × 2)$$\frac{3}{4}$$
= (24)$$\frac{3}{4}$$
= 24×$$\frac{3}{4}$$ [∵ (xa)b = xab]
= 2³
= 8

(iv) 125$$\frac{-1}{3}$$ = (5 × 5 × 5)-$$\frac{1}{3}$$
= (53)-$$\frac{1}{3}$$
= 53×-$$\frac{1}{3}$$ [∵ (xa)b = xab]
= 5-1
= $$\frac{1}{5}$$ [∵ (x-a) = $$\frac{1}{x^a}$$]

प्रश्न 3.
सरल कीजिए
(i) 2$$\frac{2}{3}$$. 2$$\frac{1}{5}$$
(ii) ($$\frac{1}{3³}$$)7
(iii) $$\frac{11^\frac{1}{2}}{11^\frac{1}{4}}$$
(iv) 71/2.81/2
हल:
(i) 2$$\frac{2}{3}$$. 2$$\frac{1}{5}$$ = 2($$\frac{2}{3}$$+$$\frac{1}{5}$$) [∵ xaxb = xa+b]
= 2$$\frac{10+3}{5}$$
= 213/15

(ii) ($$\frac{1}{3³}$$)7 = $$\frac{1}{3^{3×7}}$$ [∵ (xa)b = xab]
= $$\frac{1}{3^{21}}$$
= 3-21

(iii) $$\frac{11^\frac{1}{2}}{11^\frac{1}{4}}$$ = 11$$\frac{1}{2}$$ – $$\frac{1}{4}$$ [∵ $$\frac{x^a}{x^b} = x^{a-b}$$]

= 11$$\frac{2-1}{4}$$
= 11$$\frac{1}{4}$$

(iv) 71/2.81/2 = (7.8)$$\frac{1}{2}$$ [∵ xaya = (xy)a]
= (56)1/2