1. 07/04/2019
INDEX NOTATION

2. 07/04/2019
Guess the Number Pattern :
Square Numbers 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
100

3. 07/04/2019
Guess the Number Pattern :
Cube Numbers. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
100

4. 07/04/2019
We use index notation to show repeated multiplication by the same number.
For example,
we can use index notation to write 2 × 2 × 2 × 2 × 2 as
index or power 25
base
This number is read as ‘two to the power of five’.
25 =
2 × 2 × 2 × 2 × 2 = 32

5. 07/04/2019 Evaluate the following:
When we raise a negative number to an odd power the answer is negative.
62 =
6 × 6 = 36
34 =
3 × 3 × 3 × 3 = 81
(–5)3 =
–5 × –5 × –5 =
–125
When we raise a negative number to an even power the answer is positive.
27 =
2 × 2 × 2 × 2 × 2 × 2 × 2 =
128
(–1)5 =
–1 × –1 × –1 × –1 × –1 = –1
(–4)4 =
–4 × –4 × –4 × –4 = 64

6. (23 – 13 + 4 – 8) = (10 + 4 – 8) = (14 – 8) = (6) = 36 07/04/2019
Example
(23 – – 8) 2
= ( – 8) 2
= (14 – 8) 2
= (6) 2
= 36

7. 07/04/2019
Task
1. (38 – 27) 2
1. (3 + 5) 2
110 64
2. (14 - 5) 2
(21 – 18) 3 81 73
3. (6 x 2) - 10 2 2
9 - 5
134 16
4. (2 x 2) 3 64
( ) - 13 2 60 3
5. (2 + 1) + (2 x 1) 2 17 3
5. (3 x 4) - (3 x 1) 2
117

8. MULTIPLICATION AND DIVISION WITH INDICES
07/04/2019
MULTIPLICATION AND DIVISION WITH INDICES

9. Multiplying numbers with indices
07/04/2019
Multiplying numbers with indices
34 × 32 =
(3 × 3 × 3 × 3) × (3 × 3)
= 3 × 3 × 3 × 3 × 3 × 3
= 36
= 3(4 + 2)
73 × 75 =
(7 × 7 × 7) × (7 × 7 × 7 × 7 × 7)
= 7 × 7 × 7 × 7 × 7 × 7 × 7 × 7
= 78
= 7(3 + 5)
When we multiply two numbers with the same base, the indices are added.
What do you notice?
23 x 25
32 x 35
46 x 44
53 x 51
63 x 63
83 x 89
27 x 22
Try these… 28 37
410 54 66
812 29

10. Dividing numbers with indices
07/04/2019
Dividing numbers with indices
4 × 4 × 4 × 4 × 4
4 × 4 =
45 ÷ 42 =
4 × 4 × 4 = 43
= 4(5 – 2)
5 × 5 × 5 × 5 × 5 × 5
5 × 5 × 5 × 5 =
56 ÷ 54 =
5 × 5 = 52
= 5(6 – 4)
When we divide two numbers with the same base the indices are subtracted.
What do you notice?
27 ÷ 25
312 ÷ 35
49 ÷ 44
53 ÷ 51
623 ÷ 615
83 ÷ 89
21 ÷ 215
Try these… 22 37 45 52 68
8-6
2-14

11. 07/04/2019
Rules of indices
Multiplying
When you multiply two things with the same base, just:
ADD the powers
Leave the base the same
Dividing
When you divide two things with the same base, just:
SUBTRACT the powers

12. 07/04/2019
Zero indices
ANYTHING to the power of 0 is ALWAYS equal to 1
60 = 1
= 1
100 = 1
= 1
x0 = 1
(12y2)0 = 1

13. INDICES INCLUDING BRACKETS AND POWERS
07/04/2019
INDICES INCLUDING BRACKETS AND POWERS

14. 07/04/2019 Brackets with a power
Consider the following:
(32)3 = 3 x 3 x 3 x 3 x 3 x 3 = 36
(24)2 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 28
(53)3 = 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 = 59
When we have brackets with a single term inside and a power outside, the indices are multiplied.
What do you notice?
(22)3
(32)2
(43)4
(53)2
(6-3)2
(8-2)2
(27)-2
Try these: 26 34
412 56
6-6
8-4
2-14

15. 07/04/2019
NEGATIVE INDICES

16. 07/04/2019 Look at the following division: 3 × 3 3 × 3 × 3 × 3 = 132
32 ÷ 34 =
Using the second index law,
32 ÷ 34 = 3(2 – 4) =
3–2
That means that,
Raising a number to the power of –1 is equivalent to finding its reciprocal. 1 32
3–2 = 1 6 1 74 1 53
Similarly,
6–1 =
7–4 =
and
5–3 =

17. 1 1 2-1 means 2 2 1 1 2 2-2 means 4 1 1 3 3-2 means 9 1 1 4 4-3 means
07/04/2019 1 1 - 1
2-1 means 2 2 1 1 - 2 2
2-2 means 4 1 1 - 2 3
3-2 means 9 1 1 - 3 4
4-3 means 64 1 1
a-1 means a - 1
a-2 means a - 2

18. 07/04/2019