Download 2 = 2 • 2 • 2 • 2 = 16 - Loudoun County Public Schools

Math 6 NOTES (5.1)
Name: _________________________________
Bases, Exponents & Powers

Bases & Exponents
BASE: the common
_____________ (a factor is the
number being multiplied together)
2
4
EXPONENT: tells you how
many times the _____________
is being multiplied by itself.
24 = 2 • 2 • 2 • 2 = 16
 Powers – numbers expressed using ____________.
Symbols
Words
50
61
72
83
94
Let’s Practice… Write each power as a product of the same factor:
1)
84
____________________________________
2)
46
____________________________________
3)
25
____________________________________
4)
103
____________________________________
Write each expression in exponential form:
5)
9•9•9•9•9•9
____________________________________
6)
5•5•5
____________________________________
7)
1
1
1 1
• •
•
3
3
3 3
____________________________________
Evaluate (solve)
73
8)
9)
____________________________________
35
____________________________________
81
10)
____________________________________
 Powers of 10
Do you see a pattern?
101
=
10
=
10
The exponent represents the number
of zeros in the product.
102
=
10 x 10
=
100
103
=
10 x 10 x 10 =
For example:
1014 = The number 1 with 14 zeros
(100,000,000,000,000)
You try:
1,000
Write as the product of common factors AND evaluate
104 ________________________________

100
=
_______________
What about a number raised to the power of zero? Complete the pattern:
23 = 8
22 = 4
Do you see a pattern?
Divide by the base as the powers
decrease.
21 = 2
20 = _____
*Any number to the zero power equals _______ !
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and Intervention
Powers and Exponents
Exponent
Base
3 ⭈ 3 ⭈ 3 ⭈ 3 ⫽ 81
兵
34 ⫽
common factors
The exponent tells you how many times to use the base as a factor.
Write 63 as a product of the same factor.
The base is 6. The exponent 3 means that 6 is used as a factor 3 times.
63 ⫽ 6 ⭈ 6 ⭈ 6
Evaluate 54.
54 ⫽ 5 ⭈ 5 ⭈ 5 ⭈ 5
⫽ 625
Write 4 ⭈ 4 ⭈ 4 ⭈ 4 ⭈ 4 in exponential form.
The base is 4. It is used as a factor 5 times, so the exponent is 5.
4 ⭈ 4 ⭈ 4 ⭈ 4 ⭈ 4 ⫽ 45
Write each power as a product of the same factor.
1. 73
2. 27
3. 92
4. 154
7. 84
8. 53
Evaluate each expression.
5. 35
6. 73
Write each product in exponential form.
9. 2 ⭈ 2 ⭈ 2 ⭈ 2
10. 7 ⭈ 7 ⭈ 7 ⭈ 7 ⭈ 7 ⭈ 7
11. 10 ⭈ 10 ⭈ 10
12. 9 ⭈ 9 ⭈ 9 ⭈ 9 ⭈ 9
13. 12 ⭈ 12 ⭈ 12
14. 5 ⭈ 5 ⭈ 5 ⭈ 5
15. 6 ⭈ 6 ⭈ 6 ⭈ 6 ⭈ 6
16. 1 ⭈ 1 ⭈ 1 ⭈ 1 ⭈ 1 ⭈ 1 ⭈ 1 ⭈ 1
© Glencoe/McGraw-Hill
6
Mathematics: Applications and Concepts, Course 2
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: Skills
Powers and Exponents
Write each power as a product of the same factor.
1. 112
2. 34
3. 25
4. 93
5. 153
6. 43
7. 16
8. 174
9. 37
10. 86
11. 92
12. 82
13. 83
14. 24
15. 25
16. 63
17. 34
18. 35
19. 93
20. 112
21. 47
22. 123
23. 19
24. 104
25. 204
26. 26
Lesson 1–2
Evaluate each expression.
Write each product in exponential form.
27. 12 ⭈ 12
28. 10 ⭈ 10 ⭈ 10
29. 4 ⭈ 4 ⭈ 4 ⭈ 4 ⭈ 4
30. 9 ⭈ 9 ⭈ 9 ⭈ 9
31. 15 ⭈ 15 ⭈ 15 ⭈ 15 ⭈ 15
32. 6 ⭈ 6 ⭈ 6 ⭈ 6 ⭈ 6 ⭈ 6 ⭈ 6 ⭈ 6
© Glencoe/McGraw-Hill
7
Mathematics: Applications and Concepts, Course 2
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: Word Problems
Powers and Exponents
1. SPACE SHUTTLE The cost of each flight
of the Space Shuttle is about
$10,000,000. Write this amount in
exponential form.
2. ANIMALS The African bush elephant is
the largest land animal and weighs
about 8 tons. Write this amount in
exponential form.
3. VOLUME To find the volume of a
rectangular box you multiply the
length times the width times the
height. In a cube all sides are the same
length. If the cube has length, width,
and height of 6 inches, write the
volume as a product. Then write it in
exponential form.
4. SCIENCE A certain type of cell doubles
every hour. If you start with one cell, at
the end of one hour you would have
2 cells, at the end of two hours you
have 4 cells, and so on. The expression
2 ⫻ 2 ⫻ 2 ⫻ 2 ⫻ 2 tells you how many
cells you would have after five hours.
Write this expression in exponential
form; then evaluate it.
5. MATH Write 625 using exponents in as
many ways as you can.
6. PREFIXES Many prefixes are used in
mathematics and science. The prefix
giga in gigameter represents
1,000,000,000 meters. Write this prefix
as a power of ten.
7. LIBRARY The school library contains
94 books. How many library books are
in the school library?
8. HOT DOGS The concession stand at the
county fair sold 63 hot dogs on the first
day. How many hot dogs did they sell?
© Glencoe/McGraw-Hill
8
Mathematics: Applications and Concepts, Course 2
NAME ________________________________________ DATE ______________ PERIOD _____
Reading to Learn Mathematics
Powers and Exponents
Pre-Activity
Read the introduction at the top of page 10 in your textbook.
Write your answers below.
1. How is doubling shown in the table?
2. If the pattern continued, how much storage space would be available by
year 6?
3. What is the relationship between the number of 2s and the year?
Reading the Lesson
4. What is the difference between a power and an exponent?
5. Identify the exponent in each expression.
a. 58
c. 83
d. 8
6. Complete the sentence:
Numbers written with exponents are in __________ form, whereas
numbers written without exponents are in __________ form.
Helping You Remember
7. In the expression 67, circle the exponent in red. Then circle the power in
another color.
© Glencoe/McGraw-Hill
9
Mathematics: Applications and Concepts, Course 2
Lesson 1–2
b. 85