Main Idea and New VocabularyKey Concept: Product of Powers Example 1: Multiply PowersExample 2: Multiply MonomialsExample 3: Multiply MonomialsKey Concept: Quotient of PowersExample 4: Divide PowersExample 5: Divide PowersExample 6: Real-World Example

• Multiply and divide monomials.

• monomial

Multiply Powers

Find 85 • 8. Express using exponents.

85 • 8 = 85 81 8 = 81

= 85 + 1

The common base is 8.= 86 Add the exponents.Answer: 86

Check85 • 8 = (8 • 8 • 8 • 8 • 8) • 8

= 8 • 8 • 8 • 8 • 8 • 8 or 86

A. 42

B. 44

C. 46

D. 48

Find 44 • 42. Express using exponents.

Find f 6 • f

3.

Multiply Monomials

f 6 • f

3 = f 6 + 3 The common base is f.

= f 9 Add the exponents.

Answer: f 9

A. g7

B. g11

C. g18

D. g29

Find g2 • g9.

Multiply Monomials

Find –3x 6y

2 • 2x 4y

3.

(–3x 6y

2)(2x 4y

3) = (–3 2)(x 6 x

4) (y 2 y

3)

Use the Commutative and Associative Properties.

= (–6)(x 6 + 4) (y

2 + 3)

The common bases are x and y.

= –6x10y 5 Add the exponents.

Answer: –6x 10y

5

A. 4x 7y

B. –4x 7y

C. 4xy

D. –4xy

Find –1x 3 • –4x

4y.

Find

Divide Powers

= 47 Subtract the exponents.

Answer: 47

The common base is 4.

A. 315

B. 38

C. 32

D. 3

Find

Divide Powers

Find .

= x 2 Subtract the exponents.

Answer: x 2

The common base is x.

A. y

B. y 8

C. y 15

D. y 56

Find

BACTERIA A scientist determines that Bacteria A multiply at a rate of 98 per second. Bacteria B were determined to multiply at a rate of 95 per second. Find how many times faster Bacteria A multiply than Bacteria B.

= 9 3 Subtract the exponents.

Answer: So, Bacteria A multiply 93 or 729 times faster than Bacteria B.

The common base is 9.

A. 2 times more

B. 3 times more

C. 22 times more

D. 24 times more

PICTURES Alexi took 25 pictures on the class trip. Brittany took 24 pictures. Find how many more pictures Alexi took than Brittany.