1. 1-3 Exponents Learn to represent numbers by using exponents.

2. 1-3 Exponents Vocabulary exponent base exponential form

3. 1-3 Exponents A number is in exponential form when it is written with a base and an exponent. 73737373 Base Exponent = 7  7  7= 343 An exponent tells how many times a number called the base is used as a factor.

4. 1-3 Exponents Exponential Form10 1 Read“10 to the 1st power” Multiply10 Value10

5. 1-3 Exponents Exponential Form10 2 Read “10 squared,” or “10 to the 2nd power” Multiply 10  10 Value100

6. 1-3 Exponents Exponential Form10 3 Read “10 cubed,” or “10 to the 3rd power” Multiply 10  10  10 Value1,000

7. 1-3 Exponents Exponential Form10 4 Read“10 to the 4th power” Multiply 10  10  10  10 Value10,000

8. 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. 5454 3 is a factor 5 times. 3535

9. 1-3 Exponents Check It Out: Example 1 Write each expression in exponential form. A. 7  7  7 B. 6  6  6  6  6  6 7 is a factor 3 times. 7373 6 is a factor 6 times. 6

10. 1-3 Exponents Additional Example 2: Finding the Value of Numbers in Exponential Form Find each value. A. 2 6 B. 4 5 2626 4545 = 2  2  2  2  2  2 = 64 = 4  4  4  4  4 = 1,024

11. 1-3 Exponents Check It Out: Example 2 Find each value. A. 3 4 B. 2 5 3434 2525 = 3  3  3  3 = 81 = 2  2  2  2  2 = 32

12. 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? 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. Additional Example 3: Problem Solving Application

13. 1-3 Exponents You can draw a diagram to see how many calls are in each round. 2 Make a Plan Secretary 1st round–4 calls 2nd round–16 calls

14. 1-3 Exponents Solve 3 Notice that in each round, the number of calls is a power of 4. 1st round: 4 calls = 4 = 4 1 2nd round: 16 calls = 4  4 = 4 2 So during the 4th round, there will be 4 4 calls. 4 4 = 4  4  4  4 = 256 During the 4th round of calls, 256 families will be notified. Look Back4 Drawing a diagram helps you see how to use exponents to solve the problem.

15. 1-3 Exponents 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.

16. 1-3 Exponents You can draw a diagram to see how many calls are in each round. 2 Make a Plan Secretary 1st round–3 calls 2nd round–9 calls

17. 1-3 Exponents Solve 3 Notice that in each round, the number of calls is a power of 3. 1st round: 3 calls = 3 = 3 1 2nd round: 9 calls = 3  3 = 3 2 So during the 4th round, there will be 3 4 calls. 3 4 = 3  3  3  3 = 81 During the 4th round of calls, 81 families will be notified. Look Back4 Drawing a diagram helps you see how to use exponents to solve the problem.