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} = (8^{2})^{1/2} = 8^{2 × 1/2} = 8^{1} = 8.

(ii) 32^{1/5} = (2^{5})^{1/5} = 2^{5 × 1/5} = 2^{1} = 2.

(iii) 125^{13} = (5^{3})^{1/3} = 5^{3 × 1/3} = 5^{1} = 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} = (3^{2})^{3/2} = 3^{2 × 3/2} = 3^{3} = 27.

(ii) 32^{2/5} = (2^{5})^{2/5} = 2^{5 × 2/5} = 2^{2} = 4.

(iii) 16^{3/4} = (2^{4})^{3/4} = 2^{4 × 3/4} = 2^{3} = 8.

(iv) 125^{-1/3} = (5^{3})^{-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}.