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Multiplication
Properties
7-3
7-3 Multiplication Properties of Exponents
of Exponents
Warm Up
Lesson Presentation
Lesson Quiz
Holt
Algebra
Holt
Algebra
11
7-3 Multiplication Properties of Exponents
Warmup Day 3
Simplify.
1.
10r 5
5s 1
2
20 p

2.
5q 3
3.
21w5
15 x 6
2s
r5
4q 3
 2
p
7 x6
5w5
4sw 5
4. 
8sx 6
x6
 5
2w
3w2 y
12 wy
1
4 w3
5.
Holt Algebra 1
Then do Activities
1,2,3 on pg 458
In your math
Journal.
Simplify.
1.
10r 5
5s 1
Simplify.
1.
10r 5
5s 1
Simplify.
1.
10r 5
5s 1
20 p 2
2.  3
5q
20 p 2
2.  3
5q
20 p 2
2.  3
5q
21w5
15 x 6
21w5
15 x 6
21w5
15 x 6
3.
3.
3.
4sw 5
4. 
8sx 6
4sw 5
4. 
8sx 6
4sw 5
4. 
8sx 6
3w2 y
12 wy
3w2 y
12 wy
3w2 y
12 wy
5.
5.
5.
7-3 Multiplication Properties of Exponents
Holt Algebra 1
7-3 Multiplication Properties of Exponents
Holt Algebra 1
7-3 Multiplication Properties of Exponents
Holt Algebra 1
7-3 Multiplication Properties of Exponents
Holt Algebra 1
7-3 Multiplication Properties of Exponents
Holt Algebra 1
7-3 Multiplication Properties of Exponents
Holt Algebra 1
7-3 Multiplication Properties of Exponents
Lesson Quiz: Part I
Find the value of each expression.
1.
3,745,000
2.
0.00293
3. The Pacific Ocean has an area of about 6.4 х 107
square miles. Its volume is about 170,000,000
cubic miles.
a. Write the area of the Pacific Ocean in standard
form.
b. Write the volume of the Pacific Ocean in scientific
notation. 1.7  108 mi3
Holt Algebra 1
7-3 Multiplication Properties of Exponents
Lesson Quiz: Part II
Find the value of each expression.
4. Order the list of numbers from least to
greatest
Holt Algebra 1
7-3 Multiplication Properties of Exponents
Warm Up
Write each expression using an exponent.
1. 2 • 2 • 2 23
2. x • x • x • x
3.
Write each expression without using an
exponent.
4. 43 4 • 4 • 4
5. y2 y • y
6. m–4
Holt Algebra 1
7-3 Multiplication Properties of Exponents
Warm Up
Write each expression using an exponent.
1. 2 • 2 • 2 23
4. 22 • 24
2. x • x • x • x
5. 3 • 34
3.
6. (22)4
Write each expression without using an
exponent.
7. 43
4•4•4
2
8. y
y•y
9. m–4
Holt Algebra 1
7-3 Multiplication Properties of Exponents
Objective
Use multiplication properties of
exponents to evaluate and simplify
expressions.
Take out your notes!
Holt Algebra 1
7-3 Multiplication Properties of Exponents
You have seen that exponential expressions are
useful when writing very small or very large
numbers. To perform operations on these numbers,
you can use properties of exponents. You can also
use these properties to simplify your answer.
In this lesson, you will learn some properties that
will help you simplify exponential expressions
containing multiplication.
Holt Algebra 1
7-3 Multiplication Properties of Exponents
Add to Your Notes:
Algebraic Exponents
An Exponential - There are no negative exponents
- There are no powers raised to a power
Expression is
simplified when: - Each base appears exactly once
- No products are raised to powers
- No quotients are raised to powers
- All fractions are in simplest form
Holt Algebra 1
7-3 Multiplication Properties of Exponents
In the Textbook page_____
Holt Algebra 1
7-3 Multiplication Properties of Exponents
Products of powers with the same base can be
found by writing each power as a repeated
multiplication.
Notice the relationship between the exponents in
the factors and the exponents in the product
5 + 2 = 7.
Holt Algebra 1
7-3 Multiplication Properties of Exponents
Add to Your Notes:
Algebraic Exponents
Property Name
Product of Powers
Holt Algebra 1
Algebraic
Representation
am
·
an
=
am + n
Example
(a·a·a)·(a·a) = a·a·a·a·a
a3 · a2 = a5
7-3 Multiplication Properties of Exponents
Holt Algebra 1
7-3 Multiplication Properties of Exponents
Example 1: Finding Products of Powers
Simplify.
A.
Since the powers have the same
base, keep the base and add the
exponents.
B.
Group powers with the same base
together.
Add the exponents of powers with
the same base.
Holt Algebra 1
7-3 Multiplication Properties of Exponents
Example 1: Finding Products of Powers
Simplify.
C.
Group powers with the same base
together.
Add the exponents of powers with
the same base.
D.
Group the positive exponents and add
since they have the same base
1
Holt Algebra 1
Add the like bases.
7-3 Multiplication Properties of Exponents
Remember!
A number or variable written without an exponent
actually has an exponent of 1.
10 = 101
y = y1
Holt Algebra 1
7-3 Multiplication Properties of Exponents
Example 2: Astronomy Application
Light from the Sun travels at about
miles per second. It takes about 15,000 seconds
for the light to reach Neptune. Find the
approximate distance from the Sun to Neptune.
Write your answer in scientific notation.
distance = rate  time
mi
Holt Algebra 1
Write 15,000 in
scientific notation.
Use the Commutative
and Associative
Properties to group.
Multiply within each
group.
7-3 Multiplication Properties of Exponents
To find a power of a power, you can use the
meaning of exponents.
Notice the relationship between the exponents in
the original power and the exponent in the final
power:
Holt Algebra 1
7-3 Multiplication Properties of Exponents
Add to Your Notes:
Algebraic Exponents
Property Name
Power of a Power
Holt Algebra 1
Algebraic
Representation
(am)n = am·n
Example
(a2)(a2)(a2) =
(a·a)(a·a)(a·a) =
a·a·a·a·a·a
(a2)3 = a6
7-3 Multiplication Properties of Exponents
Holt Algebra 1
7-3 Multiplication Properties of Exponents
Example 3: Finding Powers of Powers
Simplify.
Use the Power of a Power Property.
Simplify.
Use the Power of a Power Property.
Zero multiplied by any number is
zero
1
Holt Algebra 1
Any number raised to the zero
power is 1.
7-3 Multiplication Properties of Exponents
Example 3: Finding Powers of Powers
Simplify.
C.
Use the Power of a Power Property.
Simplify the exponent of the first
term.
Since the powers have the same
base, add the exponents.
Write with a positive exponent.
Holt Algebra 1
7-3 Multiplication Properties of Exponents
Powers of products can be found by using the
meaning of an exponent.
Holt Algebra 1
7-3 Multiplication Properties of Exponents
Add to Your Notes:
Algebraic Exponents
Property Name
Power of a
Product
Holt Algebra 1
Algebraic
Representation
(ab)m = am · bm
Example
(ab)3 = (ab)(ab)(ab) =
a·b·a·b·a·b = a·a·a·
b·b·b
(ab)3 = a3 · b3
7-3 Multiplication Properties of Exponents
Example 4: Finding Powers of Products
Simplify.
A.
Use the Power of a Product Property.
Simplify.
B.
Use the Power of a Product Property.
Simplify.
Holt Algebra 1
7-3 Multiplication Properties of Exponents
Example 4: Finding Powers of Products
Simplify.
C.
Use the Power of a Product Property.
Use the Power of a Product Property.
Simplify.
Holt Algebra 1
7-3 Multiplication Properties of Exponents
Assignment Day:
• L7-3 pg 464 #4-76x4, 98-106x2
Holt Algebra 1
7-3 Multiplication Properties of Exponents
Lesson Quiz: Part I
Simplify.
1. 32• 34
2.
3. (x3)2
4.
5.
6.
7.
Holt Algebra 1
7-3 Multiplication Properties of Exponents
Lesson Quiz: Part II
7. The islands of Samoa have an approximate
area of 2.9  103 square kilometers. The area
of Texas is about 2.3  102 times as great as
that of the islands. What is the approximate
area of Texas? Write your answer in scientific
notation.
Holt Algebra 1