1. 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

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

3. 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. 2 a + 2 a = b c 2 5 + 2 5 = 4 3

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

5. Course 1 1-3 Exponents Vocabulary exponent base exponential form

6. Course 1 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.

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

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

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

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

11. 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. 5454 3 is a factor 5 times. 3535

12. Course 1 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

13. Course 1 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

14. Course 1 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

15. 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? 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

16. Course 1 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

17. Course 1 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 have been notified. Look Back4 Drawing a diagram helps you see how to use exponents to solve the problem.

18. Course 1 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.

19. Course 1 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

20. Course 1 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 x 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 have been notified. Look Back4 Drawing a diagram helps you see how to use exponents to solve the problem.

21. Course 1 1-3 Exponents Lesson Quiz Write each expression in exponential form. 1. 12  12  12 2. 9  9  9  9  9  9  9 Find each value. 3. 20 2 4. 6 4 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? 9797 12 3 400 1,296 243