Application of Laws of Indices

Solve the following

(i)            32 ^3/5                                (ii)           343 ^2/3   (iii) 64 ^2/3(iv) 0.001            (v) 14 ⁰

Solution:

1. i) 32 ^3/5 = (32 ^1/5) ³ = (⁵√32) ³

= 2 ³ = 8

1. ii) 343 ^2/3 = (343 ^1/3 )² = (³√343)²

= (7 ³)^1/3)²

= 7² = 49

iii)           64 ^2/3 = (64 ^1/3)² = (4 ³)^1/3)² = 4 ²

1. iv) (0.001)³ = (1/100)³ = (1/10)³)³ = (10 ^-3)³

= 10 ^-9 = 1/10 ⁹

1. v) 14 ⁰ = 1

EVALUATION

1)            Simplify the following

1. a) 216 ^4/3 b) 25 ⁵ c) (0.00001)²
2. d) d 32 ^2/5    e) 81 ^¾