1. Std. :- 6th
6 7
Sub. :- Mathematics
8 18
Chapter no. 8
Indices

2. The Rules Of Indices. a n x a m =……… a n  a m = ……. a - m =…….
Rule 1 : Multiplication of Indices.
a n x a m =………
Rule 4 : For Powers Of Index Numbers.
( a m ) n = …..
Rule 2 : Division of Indices.
a n  a m = …….
Rule 3 : For negative indices
a - m =…….

3. What Is An Index Number. You should know that:
We say“eight to the power of 6”.
8 6
8 x 8 x 8 x 8 x 8 x 8 =
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.
The number eight is the base number.
What are the indices in the expressions below:
(b)
(c) 8 3 x 7 2
(a) 3 x 5 4 9
3 & 2 4

4. 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 :
To simplify:
6 3 x 6 4
= (6 x 6 x 6) x (6 x 6 x 6 x 6)
(1) Expand the expression.
= 6 7
(2) How many 6’s do you now have?
Key Result.
6 3 x 6 4 = 6 7 7
(3) Now write the expression as a single power of 6.

5. Using the previous example try to simplify the following expressions:
(3) 4 11 x 4 7 x 4 8
= 8 14
= 4 26
= 3 11
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 x 4 7 as 3 and 4 are different base numbers.

6. What Goes In The Box ? 1 Simplify the expressions below :
(6) 2 2 x 2 3 x 2 5
= 2 10
(2) 9 7 x 9 2
= 9 9
(7) 8 7 x 8 10 x 8
(3) 11 6 x 11
= 8 18
(4) 14 9 x 14 12
(8) 5 20 x 5 30 x 5 50
= 14 21
= 5 100
(5) x 27 30

7. Powers Of Indices. Consider the expression below:
To appreciate this expression fully do the following:
( 2 3 ) 2
Expand the term inside the bracket.
= ( 2 x 2 x 2 ) 2
Square the contents of the bracket.
Now write the expression as a power of 2.
= ( 2 x 2 x 2 ) x (2 x 2 x 2 )
= 2 6

8. Use the result on the previous slide to simplify the following expressions:
(3)
( 8 7 ) 6
(1)
( 4 2 ) 4
(2)
( 7 5 ) 4
= 7 20
= 8 42
= 4 8
(4)
(3 2) -3
(5)
= 3 -6
We can now write down our fourth rule of index numbers:
Rule 4 : For Powers Of Index Numbers.
( a m ) n = a m n

9. What Goes In The Box ? 4
Simplify the expressions below leaving your answer as a positive index number.
(2)
(3)
(1)
(4)
(5)