Lesson #3- Exponent Laws

27Base

Power

27# of

Folds# of

SectionsExpanded Multiple

Single Exponent

1 2 2 21

2 4 2x2

3

4

5

6

7

8

Table 1- Folding Paper Experiment

What is the relationship between the # of sections and the # of folds?

# of Folds

# of Sections

Expanded MultipleSingle

Exponent

1 2 2 21

2 4 2x2 22

3 8 2x2x2 23

4 16 2x2x2x2 24

5 32 2x2x2x2x2 25

6 64 2x2x2x2x2x2 26

7 128 2x2x2x2x2x2x2 27

8 256 2x2x2x2x2x2x2x2 28

# of sections= 2# of folds

Mythbusters- Paper Foldinghttp://www.youtube.com/watch?v=kRAEBbotuIE

Question Expanded Multiple Single Exponent

31 x 32 3x3x3 33

33 x 34

52 x 54

-

When you MULTIPLY exponents of the same base...

Question Expanded Multiple Single Exponent

31 x 32 3x3x3 33

33 x 34 3x3x3x3x3x3x3 37

52 x 54 5x5x5x5x5x5 56

am x an - am+n

Keep the base and ADD the exponents.

Table 2- Multiplying Exponents of the Same Base

eg. 1 Simplify these exponents

€

70 × 712

€

37 × 3

€

97 × 96

€

47 × 4−3

€

222 × 2−20

€

−6( )7

× −6( )6

€

38

€

913

€

44

€

712

€

22

€

−6( )1

Question Expanded Quotient Single Power

34 32

25 22

43 42

am an

Question Expanded Quotient Single Power

34 32 32

25 22 23

43 42 41

am an am-n

€

(3× 3× 3× 3)

(3× 3)

€

(2 × 2 × 2 × 2 × 2)

(2 × 2)

€

(4 × 4 × 4)

(4 × 4)

€

(a× a× a× a....) {m times}

(a× a× a× a....) {n times}

Table 3- Dividing Exponents of the Same Base

When you DIVIDE exponents of the same base...

Keep the base and SUBTRACT the exponents.

€

÷

€

÷€

÷

€

÷

eg. 2 Simplify these exponents

€

712

79

€

37 ÷ 3

€

97 ÷ 96

€

47 ÷ 4−3

€

222 ÷ 2−20

€

−6( )7

−6( )6

€

36

€

91

€

410

€

73

€

242

€

−6( )1

eg. 3 Simplify these exponents

€

3a2

9a4

€

=1

3a2

€

15a5

25a2

€

=3a3

5

€

3a4

6b2×

2a2

b4×b9

a5

€

=ab3

€

÷

Homework

pg. 30 #1-3pg. 32 #4-6