Transcript Glencoe Math Connects, Course 3

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
• Write and evaluate expressions using negative
exponents.
MA.8.A.6.3 Simplify real number
expressions using the laws of exponents.
Write Expressions using Positive
Exponents
Write 4–4 using a positive exponent.
Definition of negative exponent
Answer:
Write 5–7 using a positive exponent.
A. –57
B. 57
C.
D.
Write Expressions using Positive
Exponents
Write c–7 using a positive exponent.
Definition of negative exponent
Answer:
Write r–8 using a positive exponent.
A. r8
B. –r8
C.
D.
Evaluate Expressions with
Negative Exponents
Evaluate 5–2.
Definition of negative exponent
52 = 5 • 5 or 25
Answer:
Evaluate 4–5.
A. –20
B.
C.
D.
Evaluate Expressions with
Negative Exponents
Evaluate (–8)–2.
Definition of negative exponent
(–8)2 = (–8)(–8) or 64
Answer:
Evaluate (–5)–3.
A. –125
B.
C.
D. 125
Write Expressions using Negative
Exponents
Write
as an expression using a negative
exponent.
9 = 32
= 3–2
Answer: 3–2
Definition of negative exponent
Write
as an expression using a negative
exponent.
A.
B.
C. 7–2
D. 72
Write Expressions using Negative
Exponents
Write
as an expression using a negative
exponent.
Definition of negative exponent
Answer: f –5
Write
as an expression using a negative
exponent.
A. m–6
B. –m6
C.
D.
Use Negative Exponents
SCIENCE A grain of salt weighs about 0.0001 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.
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
Multiply and Divide with Negative
Exponents
Simplify a–5 • a–3. Express using positive
exponents.
a–5 • a–3 = a–5 + (–3)
= a–8
Product of Powers
Add the exponents.
Definition of negative exponents
Answer:
Simplify x4 • x–6. Express using positive exponents.
A. x10
B. x2
C.
D.
Multiply and Divide with Negative
Exponents
Simplify
. Express using positive exponents.
Quotient of Powers
= c2
Answer: c2
Subtract the exponents.
Simplify
A. 812
B. 86
C.
D.
. Express using positive exponents.
Write 7–6 using a positive exponent.
A. –76
B. 76
C.
D.
Write (–10)–3 using a positive exponent.
A.
B.
C. –103
D. 103
Write x–5 using a positive exponent.
A.
B.
C. x5
D. (–x)5
Simplify 6–2 • 65. Express using positive exponents.
A. 6–3
B. 63
C. 6–10
D. 610
Simplify
A. 8–15
B.
8–2
C.
82
D.
815
. Express using positive exponents.
Simplify –5x2y –2 • 3x–3y5. Express using positive
exponents.
A. –15xy3
B.
C.
D.
Simplify
exponents.
A. ab
B.
C.
D.
. Express using positive
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