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) 64^1/2
(ii) 32^1/5
(iii) 125^1/3
Solution:
We have,
(i) 64^1/2 = (8²)^1/2 = 8^{2 × 1/2} = 8¹ = 8.
(ii) 32^1/5 = (2⁵)^1/5 = 2^{5 × 1/5} = 2¹ = 2.
(iii) 125¹³ = (5³)^1/3 = 5^{3 × 1/3} = 5¹ = 5.

Question 2.
Find :
(i) 9^3/2
(ii) 32^2/5
(iii) 16^3/4
(iv) 125^-1/3
Solution:
(i) 9^3/2 = (3²)^3/2 = 3^{2 × 3/2} = 3³ = 27.
(ii) 32^2/5 = (2⁵)^2/5 = 2^{5 × 2/5} = 2² = 4.
(iii) 16^3/4 = (2⁴)^3/4 = 2^{4 × 3/4} = 2³ = 8.
(iv) 125^-1/3 = (5³)^-1/3 = 5^{3 × (-1/3)}
= 5^-1 = \(\frac {1}{5}\)

Question 3.
Simplify :
(i) 2^2/3.2^1/5
(ii) \(\left(\frac{1}{3^3}\right)^7\)
(iii) \(\frac{11^{1 / 2}}{11^{1 / 4}}\)
(iv) 7^1/2.8^1/2.
Solution:
(i) We have,
2^2/3.2^1/5 = 2^{2/3 + 1/5}
= 2^{(10 + 3)/15} = 2^13/15.

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

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

(iv) 7^1/2.8^1/2 = (7 × 8)^1/2 = 56^1/2.