1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Warm Up
Multiply.
1. 3  3  3 27
2. 4  4  4 64
3. 2  2  2  2 16
4. 5  5  5  5
625

3. 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
= 43

4. Learn to represent numbers by using exponents.

5. Vocabulary
exponent
base
exponential form

6. An exponent tells how many times a number called the base is used as a factor.
A number is in exponential form when it is written with a base and an exponent.
Exponent 73
Base
= 7  7  7= 343

7. Exponential Form
101
Read
“10 to the 1st power”
Multiply 10
Value

8. Exponential Form
102
Read
“10 squared,” or
“10 to the 2nd power”
Multiply
10  10
Value
100

9. Exponential Form
103
Read
“10 cubed,” or
“10 to the 3rd power”
Multiply
10  10  10
Value
1,000

10. Exponential Form
104
Read
“10 to the 4th power”
Multiply
10  10  10  10
Value
10,000

11. 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 54
5 is a factor 4 times. 35
3 is a factor 5 times.

12. Write each expression in exponential form.
Check It Out: Example 1
Write each expression in exponential form.
A. 7  7  7
B. 6  6  6  6  6  6 73
7 is a factor 3 times. 66
6 is a factor 6 times.

13. Additional Example 2: Finding the Value of Numbers in Exponential Form
Find each value.
A. 26
B. 45 26
= 2  2  2  2  2  2
= 64 45
= 4  4  4  4  4
= 1,024

14. Check It Out: Example 2
Find each value.
A. 34
B. 25 34
= 3  3  3  3
= 81 25
= 2  2  2  2  2
= 32

15. Understand the Problem
Additional Example 3: Problem Solving Application
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? 1
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.

16. 2
Make a Plan
You can draw a diagram to see how many calls are in each round.
Secretary
1st round–4 calls
2nd round–16 calls

17. Solve 3
Notice 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 be notified.
Look Back 4
Drawing a diagram helps you see how to use exponents to solve the problem.

18. Understand the Problem
Check It Out: Example 3
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? 1
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.

19. 2
Make a Plan
You can draw a diagram to see how many calls are in each round.
Secretary
1st round–3 calls
2nd round–9 calls

20. Solve 3
Notice that in each round, the number of calls is a power of 3.
1st round: 3 calls = 3 = 31
2nd round: 9 calls = 3  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 be notified.
Look Back 4
Drawing a diagram helps you see how to use exponents to solve the problem.

21. Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems

22. Lesson Quiz
Write each expression in exponential form.
1. 12  12  12
2. 9  9  9  9  9  9  9
Find each value.
5. In a phone tree, each of 3 people will call 3 people, and then each of those will call 3 more. How many people will be called during the 5th round of calls?
123 97
400
1,296
243

23. Lesson Quiz for Student Response Systems
1. Which of the following represents 15  15  15 in exponential form?
A. 154
B. 153
C. 152
D. 151

24. Lesson Quiz for Student Response Systems
2. Which of the following represents
12  12  12  12  12  12  12 in exponential form?
A. 125
B. 126
C. 127
D. 128

25. Lesson Quiz for Student Response Systems
3. Identify the value of 402?
A. 400
B. 200
C. 1200
D. 1600

26. Lesson Quiz for Student Response Systems
4. Identify the value of 54?
A. 125
B. 225
C. 625
D. 1225

27. Lesson Quiz for Student Response Systems
5. Sarah opened a savings account, and deposited $3 on the first day. Then, each day she deposited triple the amount of the previous day for five days. How much did she deposit on the fifth day?
A. $9
B. $81
C. $243
D. $729