Sub. :- Mathematics

Indices

Std. :- 6th

Chapter no. 8

6 7

8 18

The Rules Of Indices.Rule 1 : Multiplication of Indices.

a n x a m =………

Rule 2 : Division of Indices.

a n a m = …….

Rule 4 : For Powers Of Index Numbers.

( a m ) n = …..

Rule 3 : For negative indices

a - m =…….

What Is An Index Number.You should know that:

8 x 8 x 8 x 8 x 8 x 8 = 8 6 We say“eight to the power of 6”.

The power of 6 is an index number.

The plural (more than one) of index numbers is indices.Hence indices are index numbers which are powers.

What are the indices in the expressions below:

(a) 3 x 5 4 (b) 36 9 + 34 (c) 8 3 x 7 2

4 9 3 & 2

The number eight is the base number.

Multiplication Of Indices.We know that : 7 x 7x 7 x 7 x 7 x 7 x 7 x 7 =

But we can also simplify expressions such as :

6 3 x 6 4To simplify:

(1) Expand the expression.= (6 x 6 x 6) x (6 x 6 x 6 x 6)

(2) How many 6’s do you now have?

7

(3) Now write the expression as a single power of 6.

= 6 7

Key Result.

6 3 x 6 4 = 6 7

Using the previous example try to simplify the following expressions:

(1) 3 7 x 3 4

= 3 11

(2) 8 5 x 8 9

= 8 14

(3) 4 11 x 4 7 x 4 8

= 4 26

We can now write down our first rule of index numbers:

Rule 1 : Multiplication of Indices.

a n x a m = a n + m

NB: This rule only applies to indices with a common base number. We cannot simplify 3 11 x 4 7 as 3 and 4 are different base numbers.

(6) 2 2 x 2 3 x 2 5

(7) 8 7 x 8 10 x 8

(8) 5 20 x 5 30 x 5 50

= 2 10

= 8 18

= 5 100

= 9 9

= 14 21

Simplify the expressions below :

(1) 6 4 x 6 3

(2) 9 7 x 9 2

(3) 11 6 x 11

(4) 14 9 x 14 12

(5) 27 25 x 27 30

What Goes In The Box ? 1

Powers Of Indices.Consider the expression below:

( 2 3 ) 2

To appreciate this expression fully do the following:

Expand the term inside the bracket.

= ( 2 x 2 x 2 ) 2

Square the contents of the bracket.

= ( 2 x 2 x 2 ) x (2 x 2 x 2 ) Now write the expression as a power of 2.

= 2 6

Use the result on the previous slide to simplify the following expressions:

(1) ( 4 2 ) 4 (2) ( 7 5 ) 4(3) ( 8 7 ) 6

= 4 8 = 7 20 = 8 42

(4) (3 2) -3

= 3 -6

63

1

41 )5(

(5) 443 )55( x

45We can now write down our fourth rule of index numbers:

Rule 4 : For Powers Of Index Numbers.

( a m ) n = a m n

What Goes In The Box ? 4Simplify the expressions below leaving your answer as a positive index number.

(1) 54 )7(63 )5( (2) (3) 37 )10(

(4) 342 )88( (5) 523 )77(

207 185

1 2110

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