Course 1 1-3 Exponents 1-3 Exponents Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

Course 1

1-3 Exponents1-3 Exponents

Course 1

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Course 1

1-3 Exponents

Warm UpMultiply.

1. 3 3 3

27

64

16

625

2. 4 4 4

3. 2 2 2 2

4. 5 5 5 5

Course 1

1-3 Exponents

Problem of the Day

Replace the letters a, b, and c with the numbers 3, 4, and 5 to make a true statement.2a + 2a = bc

25+ 25 = 43

Course 1

1-3 Exponents

Learn to represent numbers by using exponents.

Course 1

1-3 Exponents

Vocabulary

exponentbaseexponential form

Course 1

1-3 Exponents

A number is in exponential form when it is written with a base and an exponent.

7733Base

Exponent

= 7 7 7= 343

An exponent tells how many times a number called the base is used as a factor.

Course 1

1-3 Exponents

Exponential Form 101

Read “10 to the 1st power”

Multiply 10

Value 10

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1-3 Exponents


Read“10 squared” or “10 to the 2nd power”

Multiply 10 10

Value 100

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1-3 Exponents


Read“10 cubed” or “10 to the 3rd power”

Multiply 10 10 10

Value 1,000

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1-3 Exponents


Read “10 to the 4th power”

Multiply 10 10 10 10

Value 10,000

Course 1

1-3 Exponents

Additional Example 1: Writing Numbers in Exponential Form

Write each expression in exponential form.

A. 5 5 5 5

B. 3 3 3 3 3

5 is a factor 4 times.54


Course 1

1-3 Exponents

Check It Out: Example 1


A. 7 7 7

B. 6 6 6 6 6 6



Course 1

1-3 Exponents

Additional Example 2: Finding the Value of Numbers in Exponential Form

Find each value.

A. 26

B. 45

26

45

= 2 2 2 2 2 2

= 64

= 4 4 4 4 4

= 1,024

Course 1

1-3 Exponents


Find each value.

A. 34

B. 25

34

25

= 3 3 3 3

= 81

= 2 2 2 2 2

= 32

Course 1

1-3 Exponents

A phone tree is used to contact families at Paul’s school. The secretary calls 4 families. Then each family calls 4 other families, and so on. How many families will be notified during the fourth round of calls?

11 Understand the Problem

The answer will be the number of families called in the 4th round.

List the important information:

• The secretary calls 4 families.

• Each family calls 4 families.

Additional Example 3: Problem Solving Application

Course 1

1-3 Exponents

You can draw a diagram to see how many calls are in each round.

22 Make a Plan

Secretary

1st round – 4 calls

2nd round–16 calls

Course 1

1-3 Exponents

Solve33Notice that in each round, the number of calls is a power of 4.

1st round: 4 calls = 4 = 41

2nd round: 16 calls = 4 4 = 42

So during the 4th round, there will be 44 calls. 44 = 4 4 4 4 = 256

During the 4th round of calls, 256 families will have been notified.

Look Back44Drawing a diagram helps you see how to use exponents to solve the problem.

Course 1

1-3 Exponents


A phone tree is used to contact families at Paul’s school. The secretary calls 3 families. Then each family calls 3 other families, and so on. How many families will be notified during the fourth round of calls?

11 Understand the Problem

The answer will be the number of families called in the 4th round.

List the important information:

• The secretary calls 3 families.

• Each family calls 3 families.

Course 1

1-3 Exponents

You can draw a diagram to see how many calls are in each round.

22 Make a Plan

Secretary

1st round – 3 calls

2nd round–9 calls

Course 1

1-3 Exponents

Solve33Notice that in each round, the number of calls is a power of 3.

1st round: 3 calls = 3 = 31

2nd round: 9 calls = 3 x 3 = 32

So during the 4th round, there will be 34 calls. 34 = 3 3 3 3 = 81

During the 4th round of calls, 81 families will have been notified.

Look Back44Drawing a diagram helps you see how to use exponents to solve the problem.

Course 1

1-3 Exponents

Lesson Quiz


1. 12 12 12

2. 9 9 9 9 9 9 9

Find each value.

3. 202 4. 64

5. In a phone tree, each of three people will call

three people, and then each of those will call

three more. If there are five levels of the tree,

how many people will be called?

97

123

400 1,296

243

Course 1

1-3 Exponents1-4 Order of Operations

Course 1

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Course 1

1-3 Exponents

Warm UpPerform the operations in order from left to right.

1. 8 + 4 – 22. 9 3 + 13. 7 – 3 + 54. 20 ÷ 4 + 6

10

289

11

Course 1

1-3 Exponents

Problem of the Day

0 1 2 3 4 5 6 7 8 9 = 1Put the appropriate plus or minus signs between the numbers so that the total equals 1.

0 + 1 – 23 + 45 + 67 – 89 = 1

Course 1

1-3 Exponents

Learn to use the order of operations.

Course 1

1-3 Exponents

Vocabulary

numerical expressionsevaluateorder of operations

Course 1

1-3 Exponents

A numerical expression is a mathematical phrase that includes only numbers and operation symbols.

Numerical Expressions

4 + 8 ÷ 2 6

371 – 203 + 2 5,006 19

When you evaluate a numerical expression, you find its value.

Course 1

1-3 Exponents

When an expression has more than one operation, you must know which operation to do first. To make sure that everyone gets the same answer, we use the order of operations.

ORDER OF OPERATIONS1. Perform operations in parentheses.2. Find the values of numbers with exponents.3. Multiply or divide from left to right as ordered in the problem.4. Add or subtract from left to right as ordered in the problem.

Course 1

1-3 Exponents

The first letters of these words can help you remember the order of operations.

Please Parentheses

Excuse Exponents

My Multiply

Dear Divide

Aunt Add

Sally Subtract

Helpful Hint

Course 1

1-3 Exponents

Additional Example 1A: Using the Order of Operations

Evaluate the expression.

There are no parentheses or exponents.

15 – 5 Divide.

10 Subtract.

15 – 10 ÷ 2

15 – 10 ÷ 2

Course 1

1-3 Exponents

Additional Example 1B: Using the Order of Operations


9 + (21 ÷ 7) 5

9 + (21 ÷ 7) 5

Perform operations within parentheses.

Multiply.

9 + 3 5

9 + 15

Add. 24

Course 1

1-3 Exponents

Check It Out: Example 1A


There are no parentheses or exponents.

12 – 3 Divide.

9 Subtract.

12 – 6 ÷ 2

12 – 6 ÷ 2

Course 1

1-3 Exponents

Check It Out: Example 1B


7 + (24 ÷ 6) 3

7 + (24 ÷ 6) 3


Multiply.

7 + 4 3

7 + 12

Add. 19

Course 1

1-3 Exponents

Additional Example 2A: Using the Order of Operations with Exponents


24 + 6 4

There are no parentheses.

Multiply.

16 + 6 4

16 + 24

Add. 40

2 + 6 4 4

Find the value of the number with the exponent.

Course 1

1-3 Exponents

Additional Example 2B: Using the Order of Operations with Exponents


24 ÷ (9 – 6) 32 – 10


Multiply.

8 9 – 10

72 – 10

Divide.

62


24 ÷ (9 – 6) 32 – 10

24 ÷ 3 32 – 10

24 ÷ 3 9 – 10

Subtract.

Course 1

1-3 Exponents

Check It Out: Example 2A


42 + 3 7

There are no parentheses.

Multiply.

16 + 3 7

16 + 21

Add. 37

42 + 3 7


Course 1

1-3 Exponents

Check It Out: Example 2B


32 ÷ (8 – 4) 22 – 12


Multiply.

8 4 – 12

32 – 12

Divide.

20


32 ÷ (8 – 4) 22 – 12

32 ÷ 4 22 – 12

32 ÷ 4 4 – 12

Subtract.

Course 1

1-3 Exponents

Additional Example 3: Consumer Application

Mr. Kellett bought 6 used CDs for $4 each and 5 used CDs for $3 each. Evaluate the following expression to find the amount Mr. Kellett spent on CDs.

6 4 + 5 3

24 + 15

39

Mr. Kellett spent $39 on CDs.

Course 1

1-3 Exponents


Ms. Nivia bought 4 new CDs for $8 each and 6 used CDs for $4 each. Evaluate the following expression to find the amount Ms. Nivia spent on CDs.

4 8 + 6 4

32 + 24

56

Ms. Nivia spent $56 on CDs.

Course 1

1-3 Exponents

Lesson Quiz

Evaluate each expression.1. 15 + 4 2

2. (12 – 5)2 – 10

3. 3 + 9 2 – 5

4. 43 – 30 ÷ 2

5. Chaz bought 4 football cards for $2 each and 8 baseball cards for $3 each. Evaluate the expression to find the amount Chaz spent on cards: 4 2 + 8 3.

39

23

16

49

$32

Documents

Course 1 1-3 Exponents 1-3 Exponents Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day