Exponents 1-2 - West Windsor-Plainsboro Regional School District

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 ⫽
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⫽
4
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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.
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All rights reserved.
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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
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⫽ 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.
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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.
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Holt McDougal Mathematics