Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

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

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

Learn to represent numbers by using exponents.

Vocabulary exponent base exponential form

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

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

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

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

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

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.

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.

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

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

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.

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

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.

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.

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

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.

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

Lesson Quiz Write each expression in exponential form. 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 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

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

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

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

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

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