These NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.6 Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Exercise 1.6

Question 1.

Find

(i) \(64^{\frac{1}{2}}\)

(ii) \(32^{\frac{1}{5}}\)

(iii) \(125^{\frac{1}{3}}\)

Solution:

Question 2.

Find

(i) \(9^{\frac{3}{2}}\)

(ii) \(32^{\frac{2}{5}}\)

(iii) \(16^{\frac{3}{4}}\)

(iv) \((125)^{-\frac{1}{3}}\)

Solution:

(i) We have given

\(9^{\frac{3}{2}}=\left[(9)^{\frac{1}{2}}\right]^{3}\)

= (3)^{3}

= 27

Therefore, \((9)^{\frac{3}{2}}\) = 27

(ii) We have given,

\(32^{\frac{2}{5}}=\left[32^{\frac{1}{5}}\right]^{2}\)

= (2)^{2}

= 4

Therefore, \((32)^{\frac{2}{5}}\) = 4

(iii) We have given,

\((16)^{\frac{3}{4}}=\left[(16)^{\frac{1}{4}}\right]^{3}\)

= (2)^{3}

= 8

Therefore, \((16)^{3 / 4}\) = 8

(iv) We have given,

\((125)^{-\frac{1}{3}}=\left[(125)^{\frac{1}{3}}\right]^{-1}\)

= (5)^{-1}

= \(\frac{1}{5}\)

Therefore, \((125)^{-\frac{1}{3}}=\frac{1}{5}\)

Question 3.

Simplify

(i) \(2^{\frac{2}{3}} \cdot 2^{\frac{1}{5}}\)

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

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

(iv) \(7^{\frac{1}{2}} \cdot 8^{\frac{1}{2}}\)

Solution:

(i) We have given \(2^{\frac{2}{3}} \cdot 2^{\frac{1}{5}}\)