2. Example 4: Divide Powers
Main Idea and New Vocabulary
Key Concept: Product of Powers
Example 1: Multiply Powers
Example 2: Multiply Monomials
Example 3: Multiply Monomials
Key Concept: Quotient of Powers
Example 4: Divide Powers
Example 5: Divide Powers
Example 6: Real-World Example
Lesson Menu

3. Multiply and divide monomials.
Main Idea/Vocabulary

4. Key Concept

5. Find 85 • 8. Express using exponents.
Multiply Powers
Find 85 • 8. Express using exponents.
85 • 8 = 85  81 8 = 81
= The common base is 8.
= 86 Add the exponents.
Answer: 86
Check
85 • 8 = (8 • 8 • 8 • 8 • 8) • 8
= 8 • 8 • 8 • 8 • 8 • 8 or 86 
Example 1

6. Find 44 • 42. Express using exponents.
A. 42
B. 44
C. 46
D. 48
Example 1 CYP

7. f 6 • f 3 = f 6 + 3 The common base is f. = f 9 Add the exponents.
Multiply Monomials
Find f 6 • f 3.
f 6 • f 3 = f The common base is f.
= f 9 Add the exponents.
Answer: f 9
Example 2

8. Find g2 • g9.
A. g7
B. g11
C. g18
D. g29
Example 2 CYP

9. = (–6)(x 6 + 4) (y 2 + 3) The common bases are x and y.
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
Example 3

10. Find –1x 3 • –4x 4y.
A. 4x 7y
B. –4x 7y
C. 4xy
D. –4xy
Example 3 CYP

11. Key Concept 4

12. = 47 Subtract the exponents.
Divide Powers
Find
The common base is 4.
= 47 Subtract the exponents.
Answer: 47
Example 4

13. Find
A. 315
B. 38
C. 32
D. 3
Example 4 CYP

14. = x 2 Subtract the exponents.
Divide Powers
Find
The common base is x.
= x 2 Subtract the exponents.
Answer: x 2
Example 5

15. Find
A. y
B. y 8
C. y 15
D. y 56
Example 5 CYP

16. = 9 3 Subtract the exponents.
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.
The common base is 9.
= 9 3 Subtract the exponents.
Answer: So, Bacteria A multiply 93 or 729 times faster than Bacteria B.
Example 6

17. PICTURES Alexi took 25 pictures on the class trip
PICTURES Alexi took 25 pictures on the class trip. Brittany took 24 pictures. Find how many more pictures Alexi took than Brittany.
A. 2 times more
B. 3 times more
C. 22 times more
D. 24 times more
Example 6 CYP