# Fractional Indices

## introduction

In the previous lesson you learnt about positive indices.In this lesson you will be exposed to another aspect of indices i.e fractional indices.

# Objectives

 By the end of this lesson you should be able to i)state laws of fractional indices ii)evaluate expressions in fractional indices

## Lesson Content

In this lesson you will be learning about cases when the indices are fractions .

From previous work; $5^ \frac{1}{2} \times 5^ \frac{1}{2} = 5^{\frac{1}{2} + \frac{1}{2}}$

=51=5(from laws of positive indices)

which means that(51/2)2=5 therefore,51/2=2√5

now look at the following example $8^ \frac{1}{3} \times 8^ \frac{1}{3} \times 8^ \frac{1}{3} = 8^{\frac{1}{3} + \frac{1}{3} + \frac{1}{3}} = 8^1 =8$

Hence(81/3)3=8

therefore81/3=3√8

Similarly a1/3=3√a

In general a1/n=n√a

Consider also 82/3

Now 82/3*82/3*82/3=(82/3)3

=82/3*3/1

Now if (82/3)3=82Then 82/3=

(by taking cube roots on both sides) so in general a1/n =

Therefore you have am/n=

When m=1, then am/n=a1/n=

Examples:Evaluate the following

i) 811/4

ii) 271/3 iii)(16/25)1/2

Solutions i) 811/4 =(34))1/4=31= 3

ii)271/3=(33)1/3=31=3

iii)(16/25)1/2= (42)1/2/(52)1/2

=41/51=4/5

# Summary

 In this lesson you have been exposed to the basic laws of operating fractional indices.

# Assignment

 {{{1}}}