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Warm Up Problem of the Day Lesson Presentation Lesson Quizzes
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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
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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
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Learn to represent numbers by using exponents.
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Vocabulary exponent base exponential form
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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
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Exponential Form 101 Read “10 to the 1st power” Multiply 10 Value
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Exponential Form 102 Read “10 squared,” or “10 to the 2nd power” Multiply 10 10 Value 100
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Exponential Form 103 Read “10 cubed,” or “10 to the 3rd power” Multiply 10 10 10 Value 1,000
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Exponential Form 104 Read “10 to the 4th power” Multiply 10 10 10 10 Value 10,000
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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.
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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.
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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
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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
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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.
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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
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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.
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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.
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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
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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.
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Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems
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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
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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
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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
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Lesson Quiz for Student Response Systems
3. Identify the value of 402? A. 400 B. 200 C. 1200 D. 1600
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Lesson Quiz for Student Response Systems
4. Identify the value of 54? A. 125 B. 225 C. 625 D. 1225
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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
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