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5
7
2
1
am x an = am+n
Consider the following:
32 x 33 = 3 x 3 x 3 x 3 x 3 = 35 (base 3)
24 x 23 = 2 x 2 x 2 x 2 x 2 x 2 x 2 = 27 (base 2)
53 x 52 x 5 = 5 x 5 x 5 x 5 x 5 x 5 = 56 (base 5)
For multiplication of numbers in the same base you?
Multiplication Rule
34
base 3
index 4
53
base 5
index 3
add the indices
Generalising gives:
28
37
410
54
66
812
29
23 x 25
32 x 35
46 x 44
53 x 51
63 x 63
83 x 89
27 x 22
Write the following as a single exponent:
The Rules for Indices:
Multiplication
The Rules for Indices
Division
Consider the following:
am ÷ an = am-n
Division Rule
Generalising gives:
Using this convention for indices means that:
For division of numbers in the same base you?
subtract the indices
a0 = 1
In general:
and
Generalising gives:
Negative Index Rule
The Rules for Indices:
Powers
Consider the following:
(32)3 = 3 x 3 x 3 x 3 x 3 x 3 = 36 (base 3)
(24)2 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 28 (base 2)
(53)3 = 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 = 59 (base 5)
To raise an indexed number to a given power you?
multiply the indices
(am)n = amn
Power Rule
Generalising gives:
26
34
412
56
6-6
8-4
2-14
(22)3
(32)2
(43)4
(53)2
(6-3)2
(8-2)2
(27)-2
Write the following as a single exponent:
23
24
20
30
2-1
3-1
4-2
25 ÷ 22
26 ÷ 22
23 ÷ 23
36 ÷ 36
23 ÷ 24
35 ÷ 36
47 ÷ 49
Write the following as a single exponent and evaluate
8
16
1
1
1/2
1/3
1/16
Write the following fractions in index form.
Write the following as fractional powers.
am x an = am+n
Multiplication Rule
am ÷ an = am-n
Division Rule
a0 = 1
Negative Index Rule
a-n = 1/an