Download DM_Indices

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

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
Combining numbers
5x5x5 x2x2x2x2
= 53 x 24
We can not write this any more simply
Can ONLY do that if BASE NUMBERS are the same
Rule 1 : Multiplication
26 x 24 = 210
24 x 22 = 26
35 x 37 = 312
General Rule
am x an = am+n
Rule 2 : Division
26 ÷ 24 = 22
25 ÷ 22 = 23
35 ÷ 37 = 3-2
General Rule
am ÷ an = am-n
Multiplying powers of the same number
Copy the text below in to
your books and then answer
the questions
a) 25 x 22 =
When multiplying:
Powers of the same base
(number) are added.
c) 62 x 6 =
In general: am x an = am+n
Base number
b) 43 x 46 =
d) 84 x 83 =
e) 92 x 9 -2 =
f) 2-3 x 2 =
Power
g) 55 x 5 –7 =
h) 3 -2 x 3 =
i) 8 -2 x 8 -3 =
Give your
answer in power
form
Example:
55 x 56= 511
Answers
a) 25 x 22 =
27
b) 43 x 46 =
49
c) 62 x 6
=
63
d) 84 x 83 =
87
e) 92 x 9 –2 =
90 =
f) 2-3 x 2
=
2 -2 =
g) 55 x 5 –7 =
5 -2 =
h) 3 -2 x 3 = 3 -1 =
i) 8 -2 x 8 -3 = 8 1 =
Dividing powers of the same number
Copy the text below in
to your books and then
answer the questions
a) 25 ÷ 22
=
When dividing:
Powers of the same base
(number) are subtracted.
b) 47 ÷ 45
=
c) 62 ÷ 6
=
d) 84 ÷ 83
=
In general: am ÷ an = am - n
e) 311 ÷ 35 =
f) 2-3 ÷ 2
Base number
Power
=
g) 55 ÷ 5 –7 =
h) 11 -2 ÷ 113 =
i) 7-4 ÷ 7-3 =
Give your
answer in power
form
Example:
56 ÷ 52= 54
Answers
a) 25 ÷ 22
= 23
b) 47 ÷ 45
= 42
c) 62 ÷ 6
= 61 =
d) 84 ÷ 83
= 81 =
e) 311 ÷ 35 = 36
f) 2-3 ÷ 2
= 2 -4
g) 55 ÷ 5 –7 = 512
h) 11 -2 ÷ 113 = 11 -5
i) 7-4 ÷ 7-3 = 7-1 =
Rule 3 : Brackets
(26)2
= 26 x 26 = 212
(35)3
= 35 x 35 x 35 = 315
General Rule
(am)n = am x n
Rule 4 : Index of 0
How could you get an answer of 30?
35 ÷ 35 = 35-5 = 30
30 = 1
General Rule
a0 = 1
Putting them together?
26 x 24 = 210 = 27
23
23
35 x 37 = 312 = 38
34
34
25 x 23 = 28
24 x 22
26
= 22
Works with algebra too!
a6 x a4
b5 x b7
c5 x c3
c4
a5 x a3
a4 x a6
= a10
= b12
= c8 = c4
c4
= a8 = a-2
a10
..and a mixture…
2a3 x 3a4 = 2 x 3 x a3 x a4 = 6a7
8a6 ÷ 4a4 = (8 ÷ 4) x (a6 ÷ a4) = 2a2
2
6
28a
4
4a