1. Exponents
Course 1

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

3. Learn to represent numbers by using exponents.

4. Vocabulary
exponent
base
exponential form

5. 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

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

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

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

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

10. 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.

11. 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.

12. 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

13. 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 have been 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 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 Back 4
Drawing a diagram helps you see how to use exponents to solve the problem.