2. Key Concept: Zero and Negative Exponents
Main Idea
NGSSS
Key Concept: Zero and Negative Exponents
Example 1: Write Expressions using Positive Exponents
Example 2: Write Expressions using Positive Exponents
Example 3: Evaluate Expressions with Negative Exponents
Example 4: Evaluate Expressions with Negative Exponents
Example 5: Write Expressions using Negative Exponents
Example 6: Write Expressions using Negative Exponents
Example 7: Real-World Example: Use Negative Exponents
Example 8: Multiply and Divide with Negative Exponents
Example 9: Multiply and Divide with Negative Exponents
Five-Minute Check
Lesson Menu

3. Write and evaluate expressions using negative exponents.
Main Idea/Vocabulary

4. MA.8.A.6.3 Simplify real number expressions using the laws of exponents.
NGSSS

5. Key Concept

6. Write Expressions using Positive Exponents
Write 4–4 using a positive exponent.
Definition of negative exponent
Answer:
Example 1

7. Write 5–7 using a positive exponent.
B. 57 C. D.
Example 1 CYP

8. Write Expressions using Positive Exponents
Write c–7 using a positive exponent.
Definition of negative exponent
Answer:
Example 2

9. Write r–8 using a positive exponent.
A. r8
B. –r8 C. D.
Example 2 CYP

10. Evaluate Expressions with Negative Exponents
Definition of negative exponent
52 = 5 • 5 or 25
Answer:
Example 3

11. Evaluate 4–5.
A. –20 B. C. D.
Example 3 CYP

12. Evaluate Expressions with Negative Exponents
Definition of negative exponent
(–8)2 = (–8)(–8) or 64
Answer:
Example 4

13. Evaluate (–5)–3.
A. –125 B. C.
D. 125
Example 4 CYP

14. Write Expressions using Negative Exponents
Write as an expression using a negative exponent.
9 = 32
= 3–2 Definition of negative exponent
Answer: 3–2
Example 5

15. Write as an expression using a negative exponent.B.
C. 7–2
D. 72
Example 5 CYP

16. Write Expressions using Negative Exponents
Write as an expression using a negative exponent.
Definition of negative exponent
Answer: f –5
Example 6

17. Write as an expression using a negative exponent.
A. m–6
B. –m6 C. D.
Example 6 CYP

18. Use Negative Exponents
SCIENCE A grain of salt weighs about gram. Write the decimal as a power of 10.
Write the decimal as a fraction.
10,000 = 104
= 10–4 Definition of negative exponent
Answer: A grain of salt weighs about 10–4 gram.
Example 7

19. FISH A sea horse travels about 0. 01 mile per hour
FISH A sea horse travels about 0.01 mile per hour. Write the decimal as a power of 10.
A. 103
B. 102
C. 10–2
D. 10–3
Example 7 CYP

20. Multiply and Divide with Negative Exponents
Simplify a–5 • a–3. Express using positive exponents.
a–5 • a–3 = a–5 + (–3) Product of Powers
= a–8 Add the exponents.
Definition of negative exponents
Answer:
Example 8

21. Simplify x4 • x–6. Express using positive exponents.
A. x10
B. x2 C. D.
Example 8 CYP

22. Multiply and Divide with Negative Exponents
Simplify Express using positive exponents.
Quotient of Powers
= c2 Subtract the exponents.
Answer: c2
Example 9

23. Simplify . Express using positive exponents.
A. 812
B. 86 C. D.
Example 9 CYP

24. Write 7–6 using a positive exponent.
B. 76 C. D.
Five Minute Check 1

25. Write (–10)–3 using a positive exponent.B.
C. –103
D. 103
Five Minute Check 2

26. Write x–5 using a positive exponent.B.
C. x5
D. (–x)5
Five Minute Check 3

27. Simplify 6–2 • 65. Express using positive exponents.
A. 6–3
B. 63
C. 6–10
D. 610
Five Minute Check 4

28. Simplify . Express using positive exponents.
A. 8–15
B. 8–2
C. 82
D. 815
Five Minute Check 5

29. Simplify –5x2y –2 • 3x–3y5. Express using positive exponents.
A. –15xy3 B. C. D.
Five Minute Check 6

30. Simplify . Express using positive exponents.
A. ab B. C. D.
Five Minute Check 5

31. Which of the following correctly shows 11–3, 111, 113, 110, and 11–1 in order from least to greatest?
A. 11–1, 11–3, 110, 111, 113
B. 110, 11–3, 11–1, 111, 113
C. 113, 111, 110, 11–1, 11–3
D. 11–3, 11–1, 110, 111, 113
Five Minute Check 5