Transcript 9-3 Multiplying_and_Dividing_Monomials

Five-Minute Check (over Lesson 9–2)
Then/Now
Key Concept: Product Powers of Property
Example 1: Multiply Powers
Example 2: Multiply Monomials
Key Concept: Quotient of Powers Property
Example 3: Divide Powers
Example 4: Real-World Example: Use Powers to
Compare Values
Over Lesson 9–2
Is 51 a prime or composite number?
A. prime
B. composite
Over Lesson 9–2
Is 37 a prime or composite number?
A. prime
B. composite
Over Lesson 9–2
What is the prime factorization of 75?
A. 3 ● 25
B. 3 ● 52
C. 5 ● 5 ● 5
D. 25 ● 25 ● 25
Over Lesson 9–2
What is the prime factorization of 108?
A. 23 ● 102
B. 23 ● 32
C. 22 ● 33
D. 2 ● 3 ● 4 ● 5
Over Lesson 9–2
Factor 15x2.
A. 5 ● 5 ● 5 ● x ● x
B. 3 ● 5 ● x
C. 5 ● 5 ● 5 ● x ● x ● x
D. 3 ● 5 ● x ● x
Over Lesson 9–2
Factor –25y4z2.
A. –1 ● 25 ● y4 ● z2
B. –1 ● 5 ● 5 ● y ● y ● y ● y ● z ● z
C. –1 ● 5 ● 5 ● y4 ● z2
D. –5 ● 5 ● y ● y ● y ● y ● z ● z
You used the Commutative and Associative
Properties of Multiplication to simplify
expressions. (Lesson 1–3)
• Multiply monomials.
• Divide monomials.
Multiply Powers
A. Find 34 ● 36.
34 ● 36 = 34+6
= 310
Answer: 310
Product of Powers Property;
the common base is 3.
Add the exponents.
Multiply Powers
B. Find 78 ● 7.
78 ● 7 = 78 ● 71
7 = 71
= 78+1
Product of Powers Property;
the common base is 7.
= 79
Add the exponents.
Answer: 79
A. Find 43 ● 45.
A. 42
B. 48
C. 415
D. 4–2
B. Find 95 ● 9.
A. 95
B. 94
C. 95
D. 96
Multiply Monomials
A. Find y4 ● y.
y4 ● y = y4+1
= y5
Answer: y5
The common base is y.
Add the exponents.
Multiply Monomials
B. Find (3p4)(–2p3).
(3p4)(–2p3) = (3 ● –2)(p4 ● p3) Group the coefficients
and variables.
= (–6)(p4+3)
The common base is p.
= –6p7
Add the exponents.
Answer: –6p7
A. Find w2 ● w5.
A. w3
B. w7
C. w10
D. w–3
B. Find (–4m3)(6m2).
A. 2m5
B. –24m5
C. –24m6
D. 2m6
Divide Powers
Quotient of Powers
Property; the common
base is 4.
= 46
Answer: 46
Subtract the exponents.
Divide Powers
B.
Quotient of Powers Property;
the common base is x.
= x11
Answer: x11
Subtract the exponents.
A. 45
B. 34
C. 38
D. 48
B. Find
A. r 4
B. 14
C. r 3
D. r 5
.
Use Powers to Compare Values
CLOUDS The table shows the
approximate heights of some
clouds. About how many times
higher are some high clouds
than some low clouds?
Write a division expression.
Quotient of Powers Property
Simplify.
Answer: The high clouds are about 8 times higher than
the low clouds.
CLOUDS The table shows
the approximate heights of
some clouds. About how
many times higher are some
high clouds than some
middle clouds?
A. 2 times
B. 4 times
C. 8 times
D. 16 times