Name Class Date 1-3
Exponents
Going Deeper
Essential question: How do you use exponents to represent numbers?
CC.6.EE.1
1
EXPLORE
video tutor
Exponents
Ricardo observed the hourly growth of bacteria in a test tube and recorded his
observations in a table.
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Time (h)
Total Bacteria
0
1
1
2
2
2×2=
3
2×2×2=
4
2×2×2×2=
A
Complete the table. What pattern(s) do you see in the Total Bacteria column?
B
At 2 hours, the total is equal to the product of two 2’s.
At 3 hours, the total is equal to the product of
2’s.
At 4 hours, the total is equal to the product of
2’s.
To show a number multiplied by itself, you can write a power. A power is
an expression with an exponent and a base. For example, ​73​ ​means the product
of three 7’s:
7​ 3​ ​= 7 × 7 × 7 = 343
The base is the number
that is multiplied.
The exponent tells how
many times the base
appears in the product.
TRY THIS!
Circle the base.
1a. ​4​7​
1b.​3​5​
1d.​​( __​ 15 ​ )​​ ​
3
1c. ​2​5​
Circle the exponent.
1e. ​6​2​
Chapter 1
1f. ​10​6​
7
1g.​​( __
​ 10
  ​ )​​ ​
8
15
1h. ​9​4​
Lesson 3
REFLECT
1i.
Conjecture What do you think it means to have an exponent of 1?
For example, what is the value of ​81​ ​?
Reading Powers
7​ 2​ ​“the 2nd power of 7”​7​3​“the 3rd power of 7”
7​ ​4 ​“the 4th power of 7”​7​5​“the 5th power of 7” and so on. . .
CC.6.EE.1
2
EXAMPLE
Using Exponents to Write Expressions
Use exponents to write each expression.
A
6 × 6 × 6 × 6 × 6 × 6 × 6
What number is being multiplied?
How many times does the base appear in the product?
is the exponent.
6×6×6×6×6×6×6=
B
This number is the base.
​ __23 ​× __
​ 23 ​× __
​ 23 ​
What number is being multiplied?
This number
This number is the base.
How many times does the base appear in the product?
is the exponent.
This number
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​ _23 ​ × _​ 23 ​ × _​ 23 ​ =
TRY THIS!
Use exponents to write each expression.
2a. 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3
2c. 6
2b. 4 × 4 × 4
2d.​ __18 ​× ​ __18 ​
2e. 5 × 5 × 5 × 5 × 5 × 5
CC.6.EE.1
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EXAMPLE
Finding the Value of a Power
Find the value of each power.
A
​93​ ​
What is the base?
The exponent is 3, so the base will appear in the product 3 times.
9​ 3​ ​=
Chapter 1
×
×
=
16
Lesson 3
B
(​​  __
​ 12 ​ )​​ ​
2
What is the base?
What is the exponent?
(​​  __​ 12 ​ )​​ ​=
2
TRY THIS!
Find the value of each power.
3a. 3​ 4​ ​
3b.​1​9​
3c.​​( __​ 25 ​ )​​ ​
3
3d.​12​2​
CC.6.EE.1
4
EXPLORE
Solving Problems Using Exponents
Judah had two children. When those children grew up, each one also
had two children, who later each had two children as well. If this
pattern continues, how many children are there in the 7th generation?
You can use a diagram to model this situation. The first point at the top
represents Judah. The other points represent children. Complete the diagram
to show the 3rd generation.
Judah
1st generation
2nd generation
3rd generation
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A
How many children are in each generation?
1st
2nd
3rd
B
Do you see a pattern in the numbers above? Try to find a pattern
using exponents.
C
How is the number of children in a generation related to the
generation number?
D
How many children will be in the 7th generation?
TRY THIS!
4.
A female guinea pig has about 4 litters per year, and a typical litter consists
of 4 baby guinea pigs. How many baby guinea pigs would a typical female
have in 4 years?
Chapter 1
17
Lesson 3
pra c t i c e
Write each power.
1. the 10th power of 8
2. the 8th power of 10
3. the 11th power of __​ 12 ​
4. the 6th power of __​ 23 ​
Use exponents to write each expression.
5. 6 × 6 × 6
6. 10 × 10 × 10 × 10 × 10 × 10 × 10
7.​ __34 ​× __​ 34 ​× __​ 34 ​× ​ __34 ​× ​ __34 ​
8.​ __79 ​× __​ 97 ​× __​ 79 ​× __​ 79 ​× __​ 79 ​× __​ 79 ​× __​ 79 ​× __​ 79 ​
Find the value of each power.
9.​8​3​
10.​7​4​
11.​5​3​
14.​​( __​ 13 ​ )​​ ​
13.​​( __​ 14 ​ )​​ ​
2
12.​4​2​
(  )
15.​​( __​ 67 ​ )​​ ​
2
3
1
9  ​  ​​ ​
16.​​ ​ __
10
Write the missing exponent.
17. 100 = ​10​
18. 8 = ​2​
​
1   ​ = ​​  __
21.​ ___
( ​ 131  ​ )​​
169
​
​
22. 14 = ​14​
​
19. 25 = ​5​
​
20. 27 = ​3​
23. 32 = ​2​
​
64
 ​= ​ __
​ 89 ​  ​​
24.​ __
81
​
(  )
​
Write the missing base.
4
3
25. 1,000 =​
​​
2
29.​ __19 ​= ​
  ​​ ​
4
27. 16 = ​
​​
(  )
2
2
30. 64 = ​
2
28. 9 = ​
​​
9
31.​ __
  ​= ​
16
​​
  ​​ ​
​​
3
32. 729 = ​
​​
33. Hadley’s softball team has a phone tree in case a game is cancelled.
The coach calls 3 players. Then each of those players calls 3 players, and so on.
How many players will be notified during the 3rd round of calls?
34. Reasoning What is the value of all powers of 1? Explain.
Chapter 1
18
Lesson 3
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(  )
26. 256 = ​
Name Class 1-3
Date Name ________________________________________ Date __________________ Class__________________
OperationsPractice
and Properties
Additional
LESSON
3
Practice B: Exponents
Write each expression in exponential form.
1. 9  9
2. 7  7  7
________________________
3. 1  1  1  1  1
_______________________
4. 5  5  5  5
5. 2  2  2  2  2  2
________________________
________________________
6. 10  10  10  10
_______________________
________________________
Find each value.
7. 62
________________
5
11. 2
________________
8. 53
9. 103
________________
10. 72
_______________
4
12. 3
13. 25
________________
________________
1
14. 160
_______________
________________
Compare. Write , , or .
15. 80 ___ 71
16. 102 ___ 112
17. 82 ___ 43
18. 34 ___ 52
19. 25 ___ 92
20. 62 ___ 33
21. What whole number equals 25 when it is squared and 125 when
it is cubed?
22. Use exponents to write the number 81 three different ways.
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© Houghton Mifflin Harcourt Publishing Company
_________________________________________________________________________________________
_________________________________________________________________________________________
Chapter 1
19
3
Practice and Problem Solving
Holt McDougal Mathematics
Name ________________________________________ Date __________________ Class__________________
Operations
and Properties
Problem
Solving
3
Problem Solving: Exponents
LESSON
2. Patty Berg has won 42 major
women’s titles in golf. Write 42
in standard form.
1. The Sun is the center of our solar
system. The Sun is the star closest to
our planet. The surface temperature
of the Sun is close to 10,000°F. Write
10,000 using exponents.
____________________________________________________________
3
3. William has 3 baseball cards and
43 football cards. Write the number
of baseball cards and footballs cards
that William has.
________________________________________
4. Michelle recorded the number of
miles she ran each day last year.
She used the following expression to
represent the total number of miles:
3  3  3  3  3  3  3. Write this
expression using exponents. How
many miles did Michelle run last year?
________________________________________
________________________________________
Choose the letter for the best answer.
5. In Tyrone’s science class he is
studying cells. Cell A divides every 30
minutes. If Tyrone starts with two
cells, how many cells will he have in 3
hours?
B 32 cells
F 2 families
C 128 cells
G 4 families
D 512 cells
H 8 families
J 16 families
8. The Strahov Stadium is the largest
sports stadium in the world. It is
located in Prague, Czech Republic. Its
capacity is about 125 people. Write the
capacity of the Strahov Stadium in
standard form.
7. The Akashi-Kaiko Bridge is the
longest suspension bridge in the
world. It is located in Kobe-Naruto,
Japan and was completed in 1998.
It is about 38 feet long. Write the
approximate length of the AkashiKaiko Bridge in standard form.
F 60 people
A 6,561 feet
G 144 people
B 2,187 feet
H 20,736 people
C 512 feet
J 248,832 people
D 24 feet
Chapter 1
203
Holtand
McDougal
Mathematics
Practice
Problem
Solving
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© Houghton Mifflin Harcourt Publishing Company
A 6 cells
6. Tanisha’s soccer team has a phone
tree in case a soccer game is
postponed or cancelled. The coach
calls 2 families. Then each family calls
2 other families. How many families
will be notified during the 4th round of
calls?