Question 1. Find the Value of:

(i) 64^1/2

64^1/2 

= (8 × 8)^1/2

= (8²)^½

= 8¹ 

= 8

(ii) 32^1/5

32^1/5

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

= (2⁵)^⅕

= 2¹ 

= 2

(iii) 125^1/3

(125)^1/3

= (5 × 5 × 5)^1/3

= (5³)^⅓

= 5¹ 

= 5

Question 2. Find the value of:

(i) 9^3/2

9^3/2 

= (3 × 3)^3/2

= (3²)^3/2

= 3³ 

= 27

(ii) 32^2/5

32^2/5 

= (2 × 2 × 2 × 2 × 2)^2/5

= (2⁵)^2⁄5

= 2² 

= 4

(iii) 16^3/4

16^3/4 

= (2 × 2 × 2 × 2)^3/4

= (2⁴)^3⁄4

= 2³ 

= 8

(iv) 125^-1/3

125^-1/3 

= (5 × 5 × 5)^-1/3

= (5³)^-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 × aⁿ = a^{m + n}

= 2^13/15

(ii) (1/3³)⁷

(1/3³)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