Exponents

6³Exponent

Base

6³ is read “Six Cubed”

6³ means 6 x 6 x 6(repeated multiplication)

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 =

9

-1

-27

Tricky Integer Bases Exponents tell you how many times

to multiply the base

ab ab 1

23

ab)(2)3(

Positive Base

=

Evaluate:

Negative Base

** Now check your answer with your calculators **

-9

Evaluate:

9

Expression Expanded Form Evaluated Solution

Expression Expanded Form Evaluated Solution

(-3) -3

(-3) • (-3) 9 (-3) • (-3) • (-3) -27

(-3) • (-3) • (-3) • (-3) 81

2)3(3)3(

1)3(

4)3(

What patterns do you notice?

If you have a negative base and an odd exponent , the answer is negative.

Example:

Example:

If you have a negative base and an even exponent , the answer is positive.

Example: Example:

(-5)1 = -5

(-5)3 = -125

(-5)2 = 25

(-5)4 = 625

10113

08

4

5

1

42

35232)10(0)6(

1002)1(1

3

1625

16

125

1-1

-9

100

1

17 -7 2013)1( -1

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

Why does x0 = 1?

43 88

5

8

7

7

52 43 xx

w

w

2

12 5

432 aa

)5)(7( 2434 cabbca

))(8( 74 ww

36

3__ 63

2 xx

xx

)9)(9(

99932

936

5

832

)1(4

)1(4)3(

7837

712x

1

46w

56a

118w

6__

144

55535 cba

)6(4 55 a 1024a

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

34 )8(

567 )2(9 nm

8

43

5

)5(

7

61

2

)2(

34

81

7*7

)7(

5

1032

3

3)3(

312

936

9)9(

999

434

234

)8(8

8)8(

128

35k

3035288 nm69

625

12

13

12256p

64

77

9

1207

4

4)4( 64

57 )(k

382 )5( zw

43)4( p

246125 zw

ExpressionUsing

Positive Exponents

Value

102 102 100101 101 10100 100 1

10-1 1 . 101

1 . 10

10-2 1 . 102

1 .

100

10-3 1 . 103

1 .

1000

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

Example

= = =

=

Negative Exponents Video

5

2

2

2 3222222

22

32

1

5

2

2

2

Simplify 35 22

3

24

4

)8)(4(

432 4)4(

23

32

)(

)(

x

x

4

12 2

25664*4

16

14 2

10 X

548

123

5*5*5

5*)5(

)5)(2)(5( 735

48

31005

77

7)7(7

27

503

44

44425

15 2

4b

64

14 3

49

17 2

31225

428

1615

3)3(

3)3(3

45

3514

56

5)6(6

9

13 2

6480 4324 8*8*)8(

8

18 1

7

3

b

b