Lesson 2: Fractional Indices

=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.

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

Maina 15:42, 26 February 2007 (CET)