# HBSE 9th Class Maths Solutions Chapter 1 Number Systems Ex 1.6

Haryana State Board HBSE 9th Class Maths Solutions Chapter 1 Number Systems Ex 1.6 Textbook Exercise Questions and Answers.

## Haryana Board 9th Class Maths Solutions Chapter 1 Number Systems Exercise 1.6

Question 1.
Find :
(i) 641/2
(ii) 321/5
(iii) 1251/3
Solution:
We have,
(i) 641/2 = (82)1/2 = 82 × 1/2 = 81 = 8.
(ii) 321/5 = (25)1/5 = 25 × 1/5 = 21 = 2.
(iii) 12513 = (53)1/3 = 53 × 1/3 = 51 = 5. Question 2.
Find :
(i) 93/2
(ii) 322/5
(iii) 163/4
(iv) 125-1/3
Solution:
(i) 93/2 = (32)3/2 = 32 × 3/2 = 33 = 27.
(ii) 322/5 = (25)2/5 = 25 × 2/5 = 22 = 4.
(iii) 163/4 = (24)3/4 = 24 × 3/4 = 23 = 8.
(iv) 125-1/3 = (53)-1/3 = 53 × (-1/3)
= 5-1 = $$\frac {1}{5}$$

Question 3.
Simplify :
(i) 22/3.21/5
(ii) $$\left(\frac{1}{3^3}\right)^7$$
(iii) $$\frac{11^{1 / 2}}{11^{1 / 4}}$$
(iv) 71/2.81/2.
Solution:
(i) We have,
22/3.21/5 = 22/3 + 1/5
= 2(10 + 3)/15 = 213/15.

(ii) $$\left(\frac{1}{3^3}\right)^7=\frac{1^7}{\left(3^3\right)^7}=\frac{1}{3^{21}}$$ = 3-21

(iii) $$\frac{11^{1 / 2}}{11^{1 / 4}}=11^{1 / 2-1 / 4}=11^{(2-1) / 4}$$ = 111/4

(iv) 71/2.81/2 = (7 × 8)1/2 = 561/2.