Post on 01-Jan-2016
Exponents
6³Exponent
Base
6³ is read “Six Cubed”
6³ = 6 x 6 x 6
6³ = 216
Any base to the zero power, equals one.
Example:
Any base to the first power, equals itself.
Example:
20 = 1 50 = 1
41 = 4 71 = 7
Evaluate Exponents Evaluating Exponents: means
to find the VALUE of.Example: 3² =
-9º =
(-3)³ =
Evaluate the following:
10113
= =
= =
= =
= =
= =08
3442
35232)10(0)6(17
1
3
64
16
125
1
-1
-9
100
-7
Properties of Exponents
Complete the table in your notes and look for a pattern
Rule 1:When multiplying two numbers with the same base, keep base and add the exponents.
3³ x 3²
. x
3 x 3 x 3 x 3 x 3
3 x 3 x 3 3 x 3
737373
53
Properties of Exponents
Complete the table in your notes and look for a pattern
Rule 2:When dividing two numbers with the same base, keep base and subtract the exponents.
73
2
5
6
6
66
66666
36
Rule 3When raising a number with an exponent to a power, multiply the exponents.
(3²)³
(3²) x (3²) x (3²) (3 x 3) x (3 x 3) x (3 x 3)
3 x 3 x 3 x 3 x 3 x 3
7373
63
43 88
5
8
7
7
34 )9(
8
43
5
)5(
7
61
2
)2(
12
36
)9(
99
5
1032
3
3)3(
12
5
1010
10
9
1207
4
4)4(
434
234
)8(8
8)8(
7837129
3445
12
13
210
28
34
34
81
77
)7(
7
53
5
)2(77 7
53
5
)2(
Negative Exponents
Negative Exponents are NOT negative numbers
Negative Exponents are greater than 0, but less than one
Negative Exponents can be written as fractions and decimals
ExpressionUsing
Positive Exponents
Value
102 102 100101 101 10100 100 1
10-1 1 . 101 0.1
10-2 1 . 102 0.01
10-3 1 . 103 0.001
Example
= = = 5
2
2
2 3222222
22
32
1
Simplify 35 22
28
615
)3(
)3(*3
432 4)4(
8
3
6
6
548
123
555
5)5(
27
503
44
444
22
2
12
55
6
16
22
4
14
33
4
14
22
5
15
55
3
13
4
23
6
)6(
45
3514
56
5)6(62
2
6
16
15 5*6