2. Main Idea and New Vocabulary Key Concept: Product of Powers
Example 1: Multiply Powers
Example 2: Multiply Powers
Example 3: Multiply Powers
Key Concept: Quotient of Powers
Example 4: Divide Powers
Example 5: Divide Powers
Example 6: Real-World Example
Example 7: Simplify Expressions
Lesson Menu

3. Simplify real number expressions by multiplying and dividing monomials.
Main Idea/Vocabulary

4. Key Concept

5. Simplify 76 • 7. Express using exponents.
Multiply Powers
Simplify 76 • 7. Express using exponents.
76 • 7 = 76 • = 71
= The common base is 7.
= 77 Add the exponents.
Example 1

6. Multiply Powers Check 76 · 7 = (7 · 7 · 7  7 · 7 · 7) · 7
= 7 · 7 · 7  7 · 7 · 7 · 7
= 77 
Answer: 77
Example 1

7. Simplify 8 • 85. Express using exponents.
A. 84
B. 85
C. 86
D. 88
Example 1 CYP

8. Simplify r4 • r6. Express using exponents.
Multiply Powers
Simplify r4 • r6. Express using exponents.
r4 • r6 = r The common base is r.
= r10 Add the exponents.
Answer: r10
Example 2

9. Simplify t9 • t2. Express using exponents.
A. t4.5
B. t7
C. t11
D. t18
Example 2 CYP

10. Simplify –7x2 • 11x4. Express using exponents.
Multiply Powers
Simplify –7x2 • 11x4. Express using exponents.
–7x2 • 11x4 = (–7 • 11)(x2 • x4) Commutative and Associative Properties
= (–77)(x2 + 4) The common base is x.
= –77x6 Add the exponents.
Answer: –77x6
Example 3

11. Simplify 4n6(–2n 5). Express using exponents.
A. –8n30
B. –8n11
C. 8n30
D. 8n
Example 3 CYP

12. Key Concept 4

13. Simplify . Express using exponents.
Divide Powers
Simplify Express using exponents.
= 612 – 2 The common base is 6.
= Simply.
Answer: 610
Example 4

14. Simplify . Express using exponents.
A. 82
B. 85
C. 815
D. 8–5
Example 4 CYP

15. Simplify . Express using exponents.
Divide Powers
Simplify Express using exponents.
= a14 – 8 The common base is a.
= a6 Simply.
Answer: a6
Example 5

16. Simplify . Express using exponents.
A. h4
B. h14
C. h15
D. h20
Example 5 CYP

17. = 106 – 1 or 105 Quotient of Powers
MEASUREMENT One centimeter is equal to 10 millimeters, and one kilometer is equal to 106 millimeters. How many centimeters are in one kilometer?
10 = 101
= 106 – 1 or Quotient of Powers
Answer: There are 105 centimeters in one kilometer.
Example 6

18. MEASUREMENT One metric ton is equal to 106 grams and one hectogram is equal to 102 grams. How many times greater is a metric ton than a hectogram?
A. 103 times greater
B. 104 times greater
C. 108 times greater
D times greater
Example 6 CYP

19. = 21 • 52 • 91 Subtract the exponents. = 2 • 25 • 9 52 = 25
Simplify Expressions
Simplify
Group by common base.
= 21 • 52 • 91 Subtract the exponents.
= 2 • 25 • = 25
= 450 Simplify.
Answer: 450
Example 7

20. Simplify . Express using exponents.
A. 144
B. 1,152
C. 1,536
D. 9,116
Example 7 CYP