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^ \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=2āˆš5

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=3āˆš8

Similarly a1/3=3āˆša

In general a1/n=nāˆša

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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Reading

Access Mathematics by National Open University of Nigeria.



Maina 15:42, 26 February 2007 (CET)

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