Download Powers and Exponents - Simpson County Schools

Math
Powers and Exponents
1
What Are You Learning?
2
•
I CAN write powers as a product of the
same factor.
•
I CAN write products in exponential
form.
•
I CAN evaluate exponents.
Why Do You Need To Know This?
Exponents are used in the
real-world to represent
extremely large and small
numbers. They are also
used in solving problems.
3
Vocabulary Words
 Factors—Two
or more
numbers multiplied together to
form a product.
• 3 = 6 The
numbers 2 and 3 are factors.
 Example—2
4
Vocabulary
 Base—The
common factor or
number being multiplied.
5
•5•5•5•5
Five is the base
5
Vocabulary
 Exponent—Number
that tells how
many times the base is used as a
factor.
 4²--2
is the exponent and it shows
that 4 will be multiplied two times.
4•4
6
Name the exponent and base.
7
A.
75
B.
(-10)²
C.
-22
D.
8³
Vocabulary

Powers—Numbers expressed using
exponents.

4² and 6³ are examples of powers.

4² is read “four to the second power.”
6³ is read “six to the third power.”

8
Write each power in words
9
a.
12¹
b.
5²
c.
6³
Vocabulary
10

Squared—A number multiplied by itself two times.

4 x 4 or 4² The four is being squared.

Cubed—A number multiplied by itself three times.

2 x 2 x 2 or 2³
Write Numbers in Exponential Form
11

Exponential Form—Numbers written with
exponents.

Example 1—Write 3 · 3 · 3 in exponential
form.
3 is the base. It is used as a factor 3 times.
So, the exponent is 3.
3 · 3 · 3 = 3³
Write each expression using
exponents.
A.
5·5·5
B.
12 · 12 · 12 · 12 · 12
C.
9·9·9·9·9·9
D.
E.
12
a·b·b·a·a·b
(-3)(-3)(-3)(-3)
Write each expression using
exponents.
13
A.
r·r·r·r·s·s
B.
-2 · y · x · y
C.
(-2) · (-2) · t · t · t · t
D.
x·x·y·y·z
E.
5·5·4·2·5·4
Write the product 8 • 8 • 8
in exponential form.
4.
6%
•3
8
38
3%
14
0%
2
3.
90%
51
2.
38
8•3
83
512
83
1.
Write Powers as Products
Example 1—75
The base is 7. The exponent 5 means that 7 is
used as a factor 5 times.
75 = 7 · 7 · 7 · 7 · 7

Example 2—3²
The base is 3. The exponent 2 means the 3 is
used as a factor two times. 3² = 3 · 3

15
Your Turn
Write each power as a product of the same factor.
a.
83
16
b.
4 to the sixth power
c.
2³ · 3² · 7
d.
3 to the third power · 4 squared
Write the power 73 as a product of the
same factor.
1.
2.
3.
4.
3•3•3•3•3•3•3
7•7•7
7•3
343
90%
10%
3
•3
17
3
0%
34
•3
7
•7
•7
7
•3
•3
...
0%
Vocabulary
18

Evaluate—Find the value of an expression.

Standard Form—Numbers written without
exponents.
Write Powers in Standard Form
19

Evaluate each expression.

Example 1—25 = 2 · 2 · 2 · 2 · 2 = 32

Example 2—4³ = 4 · 4 · 4 = 64
Evaluate each expression
20
a.
10²
b.
7 to the third power
c.
54
d.
8³
e.
6 to the fourth power
Evaluate 24
1.
2.
3.
4.
2•2•2•2
8
32
16
58%
23%
16%
2
•2
•2
21
16
32
8
•2
3%
Evaluate each expression
22
a.
21 · 3²
b.
7² · 3³
c.
3 · 2² · 4³
d.
7 · 6³ · 10³
Class Work

23
Pg. 12 17-35 ODD ONLY