LESSON Exponents 1-2 Lesson Objectives Represent numbers by using exponents Vocabulary exponent (p. 10) base (p. 10) exponential form (p. 10) Additional Examples Example 1 Write each expression in exponential form. A. 5 ⫻ 5 ⫻ 5 ⫻ 5 5 is a factor 4 times. B. 3 ⫻ 3 ⫻ 3 ⫻ 3 ⫻ 3 is a factor times. Example 2 Find each value. A. 26 26 ⫽ 2 ⫻ 2 ⫻ 2 ⫻ 2 ⫻ 2 ⫻ 2 ⫽ B. 45 45 ⫽ Copyright © by Holt McDougal. All rights reserved. ⫽ 4 Holt McDougal Mathematics LESSON 1-2 CONTINUED 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 • Each family calls families. families. 2. Make a Plan You can draw a diagram to see how many calls are in each round. Secretary 1st round ⫺ 2nd round ⫺ calls calls 3. Solve Notice that in each round, the number of calls is a power of 4. 1st round: 4 calls ⫽ 4 ⫽ 41 2nd round: 16 calls ⫽ ⫽ 42 So during the fourth round, there will be 44 calls. 44 ⫽ ⫽ During the 4th round of calls, families will be notified. 4. Look Back Drawing a diagram helps you see how to use exponents to solve the problem. Copyright © by Holt McDougal. All rights reserved. 5 Holt McDougal Mathematics LESSON 1-2 CONTINUED Check It Out! 1. Write the expression in exponential form. 6⫻6⫻6⫻6⫻6⫻6⫽ 2. Find the value. 34 ⫽ 3. Problem Solving Application A phone tree is used to contact families at Emily’s work. The secretary calls 3 employees. Then each employee calls 3 other employees, and so on. How many employees will be notified during the fourth round of calls? 1. Understand the Problem The answer will be the number of employees called in the fourth round. List the important information: • The secretary calls • Each employee calls employees. employees. 2. Make a Plan 3. Solve 4. Look Back Drawing a diagram helps you see how to use exponents to solve the problem. Copyright © by Holt McDougal. All rights reserved. 6 Holt McDougal Mathematics LESSON Exponents 1-2 Lesson Objectives Represent numbers by using exponents Vocabulary exponent (p. 10) The number that indicates how many times the base is used as a factor. base (p. 10) When a number is raised to a power, the number that is used as a factor. exponential form (p. 10) A number written with a base and an exponent. Additional Examples Example 1 Write each expression in exponential form. A. 5 ⫻ 5 ⫻ 5 ⫻ 5 54 5 is a factor 4 times. B. 3 ⫻ 3 ⫻ 3 ⫻ 3 ⫻ 3 35 3 is a factor 5 times. Example 2 Find each value. A. 26 26 ⫽ 2 ⫻ 2 ⫻ 2 ⫻ 2 ⫻ 2 ⫻ 2 ⫽ 64 B. 45 45 ⫽ 4 ⴛ 4 ⴛ 4 ⴛ 4 ⴛ 4 Copyright © by Holt McDougal. All rights reserved. ⫽ 1,024 4 Holt McDougal Mathematics LESSON 1-2 CONTINUED 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 • Each family calls 4 families. families. 2. Make a Plan You can draw a diagram to see how many calls are in each round. Secretary 1st round ⫺ 4 2nd round ⫺ 16 calls calls 3. Solve 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 fourth round, there will be 44 calls. 44 ⫽ 4 ⫻ 4 ⫻ 4 ⫻ 4 ⫽ 256 During the 4th round of calls, 256 families will be notified. 4. Look Back Drawing a diagram helps you see how to use exponents to solve the problem. Copyright © by Holt McDougal. All rights reserved. 5 Holt McDougal Mathematics LESSON 1-2 CONTINUED Check It Out! 1. Write the expression in exponential form. 6 6⫻6⫻6⫻6⫻6⫻6⫽ 6 2. Find the value. 34 ⫽ 81 3. Problem Solving Application A phone tree is used to contact families at Emily’s work. The secretary calls 3 employees. Then each employee calls 3 other employees, and so on. How many employees will be notified during the fourth round of calls? 1. Understand the Problem The answer will be the number of employees called in the fourth round. List the important information: • The secretary calls 3 • Each employee calls 3 employees. employees. 2. Make a Plan Secretary 1st round – 3 calls 2nd round – 9 calls 3. Solve 3 calls ⴝ 3 ⴝ 31 9 calls ⴝ 3 ⴛ 3 ⴝ 32 34 calls ⴝ 3 ⴛ 3 ⴛ 3 ⴛ 3 ⴝ 81 During the 4th round of calls, 81 employees will be notified. 4. Look Back Drawing a diagram helps you see how to use exponents to solve the problem. Copyright © by Holt McDougal. All rights reserved. 6 Holt McDougal Mathematics
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