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
A. prime
B. composite
Is 51 a prime or composite number?
Over Lesson 9–2
A. prime
B. composite
Is 37 a prime or composite number?
Over Lesson 9–2
A. 3 ● 25
B. 3 ● 52
C. 5 ● 5 ● 5
D. 25 ● 25 ● 25
What is the prime factorization of 75?
Over Lesson 9–2
A. 23 ● 102
B. 23 ● 32
C. 22 ● 33
D. 2 ● 3 ● 4 ● 5
What is the prime factorization of 108?
Over Lesson 9–2
A. 5 ● 5 ● 5 ● x ● x
B. 3 ● 5 ● x
C. 5 ● 5 ● 5 ● x ● x ● x
D. 3 ● 5 ● x ● x
Factor 15x2.
Over Lesson 9–2
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
Factor –25y4z2.
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 Product of Powers Property; the common base is 3.
= 310 Add the exponents.
Answer: 310
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. 42
B. 48
C. 415
D. 4–2
A. Find 43 ● 45.
A. 95
B. 94
C. 95
D. 96
B. Find 95 ● 9.
Multiply Monomials
A. Find y4 ● y.
Answer: y5
y4 ● y = y4+1
The common base is y.
= y5 Add the exponents.
Multiply Monomials
B. Find (3p4)(–2p3).
Answer: –6p7
(3p4)(–2p3) = (3 ● –2)(p4 ● p3)Group the coefficients and variables.
= (–6)(p4+3)The
common base is p.
= –6p7
Add the exponents.
A. w3
B. w7
C. w10
D. w–3
A. Find w2 ● w5.
A. 2m5
B. –24m5
C. –24m6
D. 2m6
B. Find (–4m3)(6m2).
Divide Powers
Quotient of Powers Property; the common base is 4.
= 46Subtract the exponents.
Answer: 46
Divide Powers
Quotient of Powers Property; the common base is x.
Answer: x11
= x11
Subtract the exponents.
B.
A. 45
B. 34
C. 38
D. 48
A. r 4
B. 14
C. r 3
D. r 5
B. Find .
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
Answer: The high clouds are about 8 times higher than the low clouds.
Simplify.
A. 2 times
B. 4 times
C. 8 times
D. 16 times
CLOUDS The table shows the approximate heights of some clouds. About how many times higher are some high clouds than some middle clouds?