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

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 $$2^{\frac{2}{3}} \cdot 2^{\frac{1}{5}}$$

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