Transcript 2. - Kyrene School District

EXPONENTS
WARM-UP Estimate the
Following
1) 2,129 + 998 = 3000
2) 31, 231 – 1,232 = 30,000
Round the Following Numbers to the 1000’s
place
3) 34,498
4) 134,556
34,000
135,000
Do you remember “learning your doubles”
when you were in 1st grade?
2+2=
3+3=
And so on….
4+4=
5+5=
Do you remember “learning your doubles”
when you were in 1st grade? How about
this?
2x2=
3x3=
And so on….
4x4=
5x5=
9
9x3
3x3x3
3. 2  2  2  2
16
4. 5  5  5  5
625
27
TRY THESE!
Multiply.
1. 3  3  3
2. 2  2  2
3. 2  2  2  2 x 2
4. 5  5  5
27
8
32
125
SAME THING???
Multiply.
1. 3  3  3
2. 2  2  2
3. 2  2  2  2 x 2
4. 5  5  5
27
8
32
125
Learn to represent numbers by using
exponents.
Insert Lesson Title Here
Vocabulary
exponent
base
exponential form
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
3
=
7

7

7=
343
7
Exponential Form
101
Read
Multiply
“10 to the 1st power”
Value
10
10
Exponential Form
102
Multiply
“10 squared” or
“10 to the 2nd power”
10  10
Value
100
Read
Exponential Form
103
Multiply
“10 cubed” or
“10 to the 3rd power”
10  10  10
Value
1,000
Read
Exponential Form
104
Read
Multiply
“10 to the 4th power”
10  10  10  10
Value
10,000
You Try This One!
5
2 =
2x2x2x2x2
32!
WARM-UP
Write the value of 24:
in standard form?
Because 2 x 2 x 2 x 2
Write 54 in in expanded form?
16
5x5x5x5
Write 92 in standard form!
18
Write the value of 32:
81
in standard form?
6?
9
E X P O N E NT S
Write
43 in expanded form?
4x4x4
Write
43 in standard form?
64
NEVER
Add the
numbers!
E X P O N E NT S
Write
24 in expanded form?
2x2x2x2
Write
24 in standard form?
16
NEVER
Multiply the
Exponent by
the Base!
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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
3 is a factor 5 times.
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Try This: 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
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
26 = 2  2  2  2  2  2
= 64
B. 45
45 = 4  4  4  4  4
= 1,024
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Try This: Example 2
Find each value.
A. 34
34 = 3  3  3  3
= 81
B. 25
25 = 2  2  2  2  2
= 32
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.
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
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 x 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
Look Back
Drawing a diagram helps you see how to use
exponents to solve the problem.
Try This: 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.
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
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
Look Back
Drawing a diagram helps you see how to use
exponents to solve the problem.
Insert Lesson Title Here
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
Try this!
Write the value of 24:
in expanded form?
16
Write 54 in in expanded form?
5x5x5x5
Write 92 in standard form!
18
81