1. Splash Screen

2. 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
Lesson Menu

3. Is 51 a prime or composite number?
B. composite
5-Minute Check 1

4. Is 37 a prime or composite number?
B. composite
5-Minute Check 2

5. What is the prime factorization of 75?
B. 3 ● 52
C. 5 ● 5 ● 5
D. 25 ● 25 ● 25
5-Minute Check 3

6. What is the prime factorization of 108?
B. 23 ● 32
C. 22 ● 33
D. 2 ● 3 ● 4 ● 5
5-Minute Check 4

7. Factor 15x2.
A. 5 ● 5 ● 5 ● x ● x
B. 3 ● 5 ● x
C. 5 ● 5 ● 5 ● x ● x ● x
D. 3 ● 5 ● x ● x
5-Minute Check 5

8. 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
5-Minute Check 6

9. Monomial is a number, a variable, or product of a number and variable 5, x, 25x, and 100cb

10. Concept A

11. 34 ● 36 = 34+6 Product of Powers Property; the common base is 3.
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
Example 1 A

12. = 78+1 Product of Powers Property; the common base is 7.
Multiply Powers
B. Find 78 ● 7.
78 ● 7 = 78 ● = 71
= 78+1 Product of Powers Property; the common base is 7.
= 79 Add the exponents.
Answer: 79
Example 1 B

13. A. Find 43 ● 45.
A. 42
B. 48
C. 415
D. 4–2
Example 1 CYP A

14. B. Find 95 ● 9.
A. 95
B. 94
C. 95
D. 96
Example 1 CYP B

15. y4 ● y = y4+1 The common base is y. = y5 Add the exponents.
Multiply Monomials
A. Find y4 ● y.
y4 ● y = y4+1 The common base is y.
= y5 Add the exponents.
Answer: y5
Example 2 A

16. (3p4)(–2p3) = (3 ● –2)(p4 ● p3) Group the coefficients and variables.
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
Example 2 B

17. A. Find w2 ● w5.
A. w3
B. w7
C. w10
D. w–3
Example 2 CYP A

18. B. Find (–4m3)(6m2).
A. 2m5
B. –24m5
C. –24m6
D. 2m6
Example 2 CYP B

19. Concept B

20. Quotient of Powers Property; the common base is 4.
Divide Powers
Quotient of Powers Property; the common base is 4.
= 46 Subtract the exponents.
Answer: 46
Example 3

21. Quotient of Powers Property; the common base is x.
Divide Powers B.
Quotient of Powers Property; the common base is x.
= x11 Subtract the exponents.
Answer: x11
Example 3 B

22. A. 45
B. 34
C. 38
D. 48
Example 3 CYP A

23. B. Find
A. r 4
B. 14
C. r 3
D. r 5
Example 3 CYP B

24. Write a division expression.
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.
Example 4

25. CLOUDS The table shows the approximate heights of some 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
Example 4

26. End of the Lesson