Warm Up

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Warm Up
Problem of the Day
Lesson Presentation
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Warm Up Multiply. 1. 3 ? 3 ? 3
27
2. 4 ? 4 ? 4
64
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3. 2 ? 2 ? 2 ? 2
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
25 25 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.
73
7 ? 7 ? 7 343
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Exponential Form 101
Read 10 to the 1st power
Multiply 10
Value 10
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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
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5 is a factor 4 times.
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3 is a factor 5 times.
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Check It Out Example 1 Write each expression
in exponential form. A. 7 ? 7 ? 7 B. 6 ? 6 ? 6
? 6 ? 6 ? 6
7 is a factor 3 times.
73
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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Additional Example 3 Problem Solving Application
A phone tree is used to contact families at
Pauls 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?

• 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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You can draw a diagram to see how many calls are
in each round.
Secretary
1st round 4 calls
2nd round16 calls
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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.
Drawing a diagram helps you see how to use
exponents to solve the problem.
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Check It Out Example 3 A phone tree is used to
contact families at Pauls 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?

• 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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You can draw a diagram to see how many calls are
in each round.
Secretary
1st round 3 calls
2nd round9 calls
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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.
Drawing a diagram helps you see how to use
exponents to solve the problem.
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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. 3. 202 4. 64 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?
123
97
1,296
400
243