Indices.ppt

Indices low for lower secondary level

1. Pick a Number Between 2 and 9
Multiply by 2
Add 5
Multiply by 50
If you have had your birthday this
year add 1763
If you have not had your birthday
this year add 1762
Subtract your 4 digit number by the
year you were born

2. Choose a Number
Double it
Add 10
Halve it
Subtract your original number
5
5 5
5

3. 5
8
Start with a Joke
Where do mathematicians like to swim?
3
53
5
5
8
3
5
3
5
5
8
5
8
5
8

4. Learning Objective
Success Criteria
I can: Write in index form and repeated
multiplication Level 5
Multiply terms with powersLevel 6
Divide terms with powersLevel 7
To be able to use the index laws of
multiplication and division

5. Indices is the mathematical term for “power”
Indices is the plural term for the singular term ‘Index’
They can be numbers or letters and float happily in the air next to a base number or letter4
5
The base
The index or power
Indices (powers) only
apply to the
number/letter (base)
to the left of it
Do not multiply the
base with the power
A BIG No NoNo!
Indices

6. Introduction
What does 4
2
actually mean?
4×4 16

7. Introduction
What does 4
5
actually mean?
4×4×4×4×4

8. Introduction
How can we write 5×5×5×5
5
4
This is 5×5×5×5 written in INDEX FORM

9. Writing in Index Form
Write the following in Index Form
•8×8×8×8 =
•3×3×3×3×3×3 =
•9×9×9 =
8
4
3
6
9
3

10. Indices
•3 x 3 x 3 x 3
•3 x 3 x 3
•3 x 3
•3
= 3
4
= 3
3
= 3
2
= 3
1

11. Learning Objective
Success Criteria
I can: Write in index form and repeated
multiplication Level 5
Multiply terms with powersLevel 6
Divide terms with powersLevel 7
To be able to use the index laws of
multiplication and division

12. Multiplying Indices
Simplify the following leaving in index
form.
•8
3
×8
4
=8×8×8×8×8×8×8
= 8
7
Is there a quick way you can work this out?
8
4
8
3

13. Investigation
Write out as a repeated multiplication
Combine together and count how many
Re-write in index form
What do you notice?

14. Multiplying Indices
Simplify the following leaving in index
form.
•8
3
×8
4
=8×8×8×8×8×8×8
= 8
7
Is there a quick way you can work this out?
•8
3
×8
4
=
4
8 = 8
7+3
8
4
8
3
Remember this only works for numbers with the
Same base number

15. Multiplying Indices
Simplify the following leaving in index
form.
•5
2
×5
4
=5×5×5×5×5×5
= 5
6
The Quick Way!!!
•5
2
×5
4
=
4
5 = 5
6+2
5
4
5
2
Remember this only works for numbers with the
Same base number

16. Am I Correct?

17. Indices with Letters
•a x a x a x a
•a x a x a
•a x a
•a
= a
4
= a
3
= a
2
= a
1

18. Multiplying Indices
Simplify the following leaving in index
form.
•a
3
×a
4
=a ×a ×a×a ×a ×a ×a
= a
7
Is there a quick way you can work this out?
•a
3
×a
4
=
4
a = a
7+3
a
4
a
3
Remember this only works for numbers with the
Same base number

19. 0
1a Anythingto the power of zero is 1!
Examples0
1 = x 0
17 = 1 0
5 5 51 x  
The Zero Power (Index)

20. Questions
Simplify the following numbers, leaving your answers in
index form:
1.(a)2
3
x 2
2
(b)3
5
x 3
2
(c)7
3
x 7(d)9
5
x 9
2
2
5
3
7
7
4
9
7
2.(a)a
3
x a
2
(b)a
5
xa
6
(c)a xa
3
(d)a
2
xa
12
a
5
a
11
a
4
a
14
3.(a)3
3
x 3
0
(b)a
0
xa
6
(c)a xa
0
(d)a
0
xa
0
3
3
a
6
a 1

21. Learning Objective
Success Criteria
I can: Write in index form and repeated
multiplication Level 5
Multiply terms with powersLevel 6
Divide terms with powersLevel 7
To be able to use the index laws of
multiplication and division

22. Dividing Indices
Simplify the following leaving in index
form.
1.2
5
÷2
2
=
= 2
3
The Quick Way!!!
2
2
2
5 2
5
2
2
=
2x2x2x2x2
2x2
1.2
5
÷2
2
=
2
2 = 2
3
-
5
Remember this only works for numbers with the
Same base number

23. Questions
Simplify the following numbers, leaving your answers in
index form:
a a
3
a
2
a
3
3.(a) (b) (c) (d)
b
3
b
7
1 2b
2.(a)a
3
÷a
2
(b)a
5
÷a
2
(c)a
3
÷a(d)a
9
÷a
3
1.(a) (b) (c) (d)
2 3
3
7
2
9
3

24. At this point, it doesn’t
make sense to say “The
product of -1 threes”.
We’ll have to use a
different approach!
3
3
= 27
3
2
= 9
3
1
= 3
3
0
= 1
3
-1
=
3
-2
=
1
3
1
9
?
?
Is there a pattern
we can see that will
help us out?
Zero and negative indices
?

25. Quickfire Questions
Without using calculator, Find The value of the following.
?
?
?
?
?
?
?
?
?

26. Exercise 1.1 (page 4-5)
You only do no
1 a,d
2a,b,c
3a,c
4, a,e
5 d,e
6a,f,I
7,8 an11

27. Learning Objective
Success Criteria
I can: Write in index form and repeated
multiplication Level 5
Multiply terms with powersLevel 6
Divide terms with powersLevel 7
To be able to use the index laws of
multiplication and division

28. Indices
Simplify the following leaving in index
form.
1.((2
3
)
For these it is best to write them out!
2
2
3
x 2
3
This means this = 2
6
Remember this only works for numbers with the
Same base number

29. Indices
Simplify the following leaving in index
form.
1.((3
5
)
For these it is best to write them out!
3
3
5
x 3
5
x 3
5
This means this = 3
15
Remember this only works for numbers with the
Same base number

30. Questions
Simplify the following numbers, leaving your answers in
index form:
1.(a)(2
3
)
2
(b)(3
5
)
2
(c)(7
3
)
3
(d)(9
2
)
5
a
6
a
10
a
9
a
10
1 1 1 1
2.(a)(a
3
)
2
(b)(a
5
)
2
(c)(a
3
)
3
(d)(a
2
)
5
2
6
3
10
7
9
9
10
3.(a)(5
0
)
2
(b)(a
0
)
3
(c)(5
3
)
0
(d)(a
2
)
0

31. Indices with Letters
6a
3
x3a
2
=6xaxaxax
=6x3x
=18a
5
3xaxa6a
3
3a
2
axaxaxa x a
6a
3
x3a
2
6a
3
3a
2
The Quick Way!!!
=x x
23
a
+
=18a
5

32. Indices with Letters
3a
5
x2a
3
= x
=3x2x
=6a
8
3a
5
2a
3
axaxax
3 xa xa xa xa xa2 xa xa
xaxa axa

33. Questions
Simplify the following numbers, leaving your answers in
index form:
a
6
a
10
a
9
a
10
3.(a)3b
3
x 7b
5
(b) (c) (d)5b x 2b
7
2b
3
x 6b
3
2b
3
x 15b
2
21b
8
10b
8
12b
6
30b
5
2
6
3
10
7
9
9
10
2.(a)(a
3
)
2
(b)(a
5
)
2
(c)(a
3
)
3
(d)(a
2
)
5