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The Rules for
Multiplication
Exponents:index 3
index 4
base 5
4
3
3
5
base 3
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?
Generalising gives:
Multiplication Rule
add the
exponents
am x an = am+n
Write the following as a single exponent:
23 x 2 5
32 x 3 5
46 x 4 4
53 x 5 1
63 x 6 3
83 x 8 9
2 7 x 22
28
37
410
54
66
812
29
The Rules for
Exponents
Consider the following:
35  32 
3x 3x 3x 3x 3
 33
3x 3
24  23 
Division
47  43 
4x 4x 4x 4x 4x 4x 4
 44
4x 4x 4
2x 2x 2x 2
 21
2x 2x 2
For division of numbers in the same base you?
Generalising gives:
Division Rule
subtract the
exponents
am  an = am-n
Using this convention for exponents means:
5x 5x 5x 5
3x 3x 3x 3
1
2
54  54 
 1  50
34  36 


3
5x 5x 5x 5
3x 3x 3x 3x 3x 3 32
7x 7x 7
73  7 3 
 1  70
1
6x 6x 6
63  67 
 4  64
7x 7x 7
6x 6x 6x 6x 6x 6x 6 6
Generalising gives:
1
n
0 = 1
a

a
In general:
Negative Exponent
an
Rule
and
Power of a
Power
The Rules for
Exponents:
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 a power to a power you?
Generalising gives:
multiply the
exponents
Power Rule
(am)n = amn
Write the following as a single exponent:
(22)3
(32)2
(43)4
(53)2
(6-3)2
(8-2)2
(27)-2
26
34
412
56
6-6
8-4
2-14