# Class 9 NCERT Solutions – Chapter 1 Number System – Exercise 1.6

**Question 1. Find the Value of:**

**(i) 64 ^{1/2}**

64

^{1/2}= (8 × 8)

^{1/2}= (8

^{2})^{½}= 8

^{1}= 8

**(ii) 32 ^{1/5}**

32

^{1/5}= (2 x 2 x 2 x 2 x 2)

^{1/5}= (2

^{5})^{⅕}= 2

^{1}= 2

**(iii) 125 ^{1/3}**

(125)

^{1/3}= (5 × 5 × 5)

^{1/3}= (5

^{3})^{⅓}= 5

^{1}= 5

**Question 2. Find the value of:**

**(i) 9 ^{3/2}**

9

^{3/2}= (3 × 3)

^{3/2}= (3

^{2})^{3/2}= 3

^{3}= 27

**(ii) 32 ^{2/5}**

32

^{2/5}= (2 × 2 × 2 × 2 × 2)

^{2/5}= (2

^{5})^{2⁄5}= 2

^{2}= 4

**(iii) 16 ^{3/4}**

16

^{3/4}= (2 × 2 × 2 × 2)

^{3/4}= (2

^{4})^{3⁄4}= 2

^{3}= 8

**(iv) 125 ^{-1/3}**

125

^{-1/3}= (5 × 5 × 5)

^{-1/3}= (5

^{3})^{-1⁄3}= 5

^{-1}= 1/5

**Question 3. Simplify the followings:**

**(i) 2 ^{2/3} × 2^{1/5}**

2

^{2/3 }× 2^{1/5}= 2

^{(2/3) + (1/5) }⸪ As,a^{m }× a^{n }= a^{m + n}= 2

^{13/15}

**(ii) (1/3 ^{3})^{7}**

(1/3

^{3})^{7}= (3

^{-3})^{7}⸪ As,(a^{m})^{n}= a^{m x n}= 3

^{-21}

**(iii) 11 ^{1/2}/11^{1/4}**

11

^{1/2}/11^{1/4}= 11

^{(1/2) – (1/4) }⸪ As,a^{m}× a^{-n}= a^{m – n}= 11

^{1/4}

**(iv) 7 ^{1/2 }× 8^{1/2}**

7

^{1/2 }× 8^{1/2}= (7 × 8)

^{1/2 }⸪ As,a^{m}× b^{m}= (a × b)^{m}= 56

^{1/2}