# 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

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