# Lesson 2: Fractional Indices

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# 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^{1}=5(from laws of positive indices)

which means that(5^{1/2})^{2}=5 therefore,5^{1/2}=2ā5

now look at the following example

Hence(8^{1/3})^{3}=8

therefore8^{1/3}=3ā8

Similarly a^{1/3}=3āa

In general a^{1/n}=nāa

Consider also 8^{2/3}

Now 8^{2/3}*8^{2/3}*8^{2/3}=(8^{2/3})^{3}

=8^{2/3*3/1}

Now if (8^{2/3})^{3}=8^{2}Then 8^{2/3}=

(by taking cube roots on both sides) so in general a^{1/n} =

Therefore you have a^{m/n}=

When m=1, then a^{m/n}=a^{1/n}=

Examples:Evaluate the following

i) 81^{1/4}

ii) 27^{1/3} iii)(16/25)^{1/2}

Solutions i) 81^{1/4} =(3^{4)})^{1/4}=3^{1}= 3

ii)27^{1/3}=(3^{3)}^{1/3}=3^{1}=3

iii)(16/25)^{1/2}= (4^{2})^{1/2}/(5^{2})^{1/2}

=4^{1}/5^{1}=4/5

Maina 15:42, 26 February 2007 (CET)