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?