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1-3 Exponents
Exponents
Warm Up
Problem of the Day
Lesson Presentation
Course
Course
11
1-3 Exponents
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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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.
2a + 2a = bc
25+ 25 = 43
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1-3 Exponents
Learn to represent numbers by using
exponents.
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1-3 Exponents
Vocabulary
exponent
base
exponential form
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1-3 Exponents
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
Base
Course 1
3
=
7

7

7=
343
7
1-3 Exponents
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Exponential Form
101
Read
Multiply
“10 to the 1st power”
Value
10
10
1-3 Exponents
Exponential Form
Multiply
“10 squared” or
“10 to the 2nd power”
10  10
Value
100
Read
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102
1-3 Exponents
Exponential Form
Multiply
“10 cubed” or
“10 to the 3rd power”
10  10  10
Value
1,000
Read
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103
1-3 Exponents
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Exponential Form
104
Read
Multiply
“10 to the 4th power”
10  10  10  10
Value
10,000
1-3 Exponents
Additional Example 1: Writing Numbers in
Exponential Form
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
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3 is a factor 5 times.
1-3 Exponents
Check It Out: Example 1
Write each expression in exponential form.
A. 7  7  7
73
7 is a factor 3 times.
B. 6  6  6  6  6  6
66
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6 is a factor 6 times.
1-3 Exponents
Additional Example 2: Finding the Value of
Numbers in Exponential Form
Find each value.
A. 26
26 = 2  2  2  2  2  2
= 64
B. 45
45 = 4  4  4  4  4
= 1,024
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1-3 Exponents
Check It Out: Example 2
Find each value.
A. 34
34 = 3  3  3  3
= 81
B. 25
25 = 2  2  2  2  2
= 32
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1-3 Exponents
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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1-3 Exponents
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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1-3 Exponents
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 4th round, there will be 44 calls.
44 = 4  4  4  4 = 256
During the 4th round of calls, 256 families will
have been notified.
4
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Look Back
Drawing a diagram helps you see how to use
exponents to solve the problem.
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.
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1-3 Exponents
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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1-3 Exponents
3
Solve
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 x 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
have been notified.
4
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Look Back
Drawing a diagram helps you see how to use
exponents to solve the problem.
1-3 Exponents
Lesson Quiz
Write each expression in exponential form.
1. 12  12  12
123
2. 9  9  9  9  9  9  9
97
Find each value.
3. 202 400
4. 64
1,296
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? 243
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