1. What are Indices?
Indices provide a way of writing numbers in a more convenient form
Indices is the plural of Index
An Index is often referred to as a power

2. For example 5 x 5 x 5 = 53 2 x 2 x 2 x 2 = 24 7 x 7 x 7x 7 x 7 = 75
5 is the INDEX
7 is the BASE NUMBER
75 & 24 are numbers in INDEX FORM

3. Combining numbers 5 x 5 x 5 x 2 x 2 x 2 x 2 = 53 x 24
We can not write this any more simply
Can ONLY do that if BASE NUMBERS are the same

4. Rule 1 : Multiplication 26 x 24 = 210 24 x 22 = 26 35 x 37 = 312
General Rule
am x an = am+n

5. Rule 2 : Division 26 ÷ 24 = 22 25 ÷ 22 = 23 35 ÷ 37 = 3-2 General Rule
am ÷ an = am-n

6. Multiplying powers of the same number
Copy the text below in to your books and then answer the questions
25 x =
43 x =
62 x =
84 x =
92 x =
2-3 x 2 =
55 x 5 –7 =
3 -2 x =
8 -2 x 8 -3 =
Give your answer in power form
Example:
55 x 56= 511
When multiplying:
Powers of the same base (number) are added.
In general: am x an = am+n
Base number
Power

7. Answers 25 x 22 = 43 x 46 = 62 x 6 = 84 x 83 = 92 x 9 –2 = 2-3 x 2 =27 49 63 87
90 =
2 -2 =
5 -2 =
3 -1 =
8 1 =

8. Dividing powers of the same number
Copy the text below in to your books and then answer the questions
25 ÷ =
47 ÷ =
62 ÷ =
84 ÷ =
311 ÷ =
2-3 ÷ 2 =
55 ÷ 5 –7 =
11 -2 ÷ 113 =
7-4 ÷ =
Give your answer in power form
Example:
56 ÷ 52= 54
When dividing:
Powers of the same base (number) are subtracted.
In general: am ÷ an = am - n
Base number
Power

9. Answers 25 ÷ 22 = 47 ÷ 45 = 62 ÷ 6 = 84 ÷ 83 = 311 ÷ 35 = 2-3 ÷ 2 =
25 ÷ =
47 ÷ =
62 ÷ =
84 ÷ =
311 ÷ =
2-3 ÷ 2 =
55 ÷ 5 –7 =
11 -2 ÷ 113 =
7-4 ÷ = 23 42
61 =
81 = 36
2 -4
512
11 -5
7-1 =

10. Rule 3 : Brackets (26)2 = 26 x 26 = 212 (35)3 = 35 x 35 x 35 = 315
General Rule
(am)n = am x n

11. Rule 4 : Index of 0 How could you get an answer of 30? 35 ÷ 35 = 35-5
= 30
30 = 1
General Rule
a0 = 1

12. Putting them together? 26 x 24 23 = 210 23 = 27 35 x 37 34 = 312 34
= 38
25 x 23
24 x 22
= 28 26
= 22

13. Works with algebra too! a6 x a4 = a10 b5 x b7 = b12 c5 x c3 c4 = c8 c4

14. 8a6 4a4 2 2 ..and a mixture… 2a3 x 3a4 = 2 x 3 x a3 x a4 = 6a7