Powers and Exponent Laws

CHAPTER 2

Chapter 2

2.1 – WHAT IS A POWER?

2.2 – POWERS OF TEN AND THE ZERO

EXPONENT

Khan Academy on Exponents

Squares Cubes

WHAT IS A POWER?

A = L2

A = 52 = 25

V = L3

V = 53 = 125

POWERS

53

Base: The number that is being repeatedly multiplied by itself.

Exponent: The number of times that the base will be multiplied by itself.

Power: The expression of the base and the exponent.

POWERS

Examples:

53 = 5 x 5 x 5

35 = 3 x 3 x 3 x 3 x 3

What about negatives? How will they work?

Are (–3)4 and –34 the same?

(–3)4 = (–3) x (–3) x (–3) x (–3) = 81

–34 = –(3 x 3 x 3 x 3) = –81

CHALLENGE

1 2 3 4 5Use these five numbers to make an expression that represents the largest possible number. You can use any operation you like (addition, subtraction, multiplication, division, exponents), but you can only use each number once.

POWERS OF TEN AND THE ZERO EXPONENT

What’s easier to write, 100000000000000000000 or 1020?

Number in Words Standard Form Power

one million 1 000 000 106

one hundred thousand 100 000 105

ten thousand 10 000 104

one thousand 1 000 103

one hundred 100 102

ten 10 101

one 1 100

ZERO EXPONENT

Power Number

44 256

43 64

42 16

41 4

40 1

You can try this with other bases, but the result will always be the same.

The Zero Exponent Law: Any base to the power of zero will be equal to one.

EXAMPLE

Write 3045 using powers of ten.

3045 = 3000 + 40 + 5= (3 x 1000) + (4 x 10) + (5

x 1)= (3 x 103) + (4 x 101) + (5 x

100)

KHAN VIDEO 2

Khan Video 2

Independent Practice

PG. 55-57 # 4, 5, 7-9 (ACE), 13, 17, 21, 22,

23 PG. 61-62 # 4, 6, 9,

13, 14

Chapter 2

2.3 – ORDER OF OPERATIONS WITH

POWERS

2.4 – EXPONENT LAWS I

ORDER OF OPERATIONS

What’s the acronym used to remember the order of operations?

B E D M A S Brackets

ExponentsDivisionMultiplicatio

nAdditionSubtraction

EXAMPLE

Calculate each expression:

33 + 23 (3 + 2)3

33 + 23 = 27 + 8

= 35

Exponents come before Addition in BEDMAS, so we do them first.

(3 + 2)3 = 53

= 125Brackets come before Exponents in BEDMAS, so we do them first.

EXPONENT RULES

Try to solve by expanding into repeated multiplication form:

73 x 74 = (7 x 7 x 7) x (7 x 7 x 7 x 7)= 7 x 7 x 7 x 7 x 7 x 7 x 7= 77

What happens? What kind of rule can we make about the multiplication of powers with like bases?

Exponent Laws:

am x an = am+n

EXPONENT RULES

What about division? Try solving this one to make a general rule:

What’s the general rule we can make for exponent division?

Exponent Laws:

EXAMPLE

Write each expression as a power.

a) 65 x 64 b) (–9)10 ÷ (–9)6

a) 65 x 64 = 65+4

= 69

b) (–9)10 ÷ (–9)6 = (–9)10-6

= (–9)4

Evaluate:

32 x 34 ÷ 33

32 x 34 ÷ 33 = 32+4-3

= 33

= 27

EXAMPLE

Evaluate.

a) 62 + 63 x 62 b) (–10)4[(–10)6 ÷ (–10)4] – 107

a) Remember, BEDMAS, so we do multiplication first before addition.

62 + 63 x 62 = 62 + 63+2

= 62 + 65

= 36 + 7776 = 7812

b) Remember, BEDMAS, so we do inside the brackets, then multiplication, then subtraction.

(–10)4[(–10)6 ÷ (–10)4] – 107 = (–10)4[(–10)2] – 107

= (–10)4+2 – 107 = (–10)6 – 107 = 1 000 000 – 10 000 000= –9 000 000

Independent Practice

PG. 66-68, # 7, 10, 12, 13, 16, 20, 24,

26

PG. 76-78, # 4ACE, 5ACE, 8, 12, 13, 15,

20

Chapter 22.5 – EXPONENT

LAWS II

HANDOUT: TRY TO FILL IN THE CHART

A POWER TO A POWER

From what we’ve learned from the chart, what can we say about the following expression:

(33)5 =

33 x 33 x 33 x 33 x 33 = 315

Exponent Laws:

EXPONENT LAWS

What about something like this? Try it!

(4 x 3)6= (4 x 3)(4 x 3)(4 x 3)(4 x 3)(4 x 3)(4 x 3)

= (4 x 4 x 4 x 4 x 4 x 4)(3 x 3 x 3 x 3 x 3 x 3)

= 46 x 36

What’s the basic rule that we can say about the what happens when we take a product or quotient to a power?

Exponent Laws:

EXAMPLE

Evaluate:

a) –(24)3 b) (3 x 2)2 c) (78 ÷ 13)3

a) –(24)3 = –24x3

= –212

= –4096

b) (3 x 2)2 = 32 x 22

= 9 x 4 = 36

c) (78 ÷ 13)3 = (6)3

= 216

Simplify, then evaluate:

(6 x 7)2 + (38 ÷ 36)3

(6 x 7)2 + (38 ÷ 36)3 = (42)2 + (32)3 = 422 + 36

= 1764 + 729 = 2493

Independent Practice

PG. 84-86, # 8, 11, 13, 14, 16, 19, 20