pre-algebra 2-8 look for a pattern in integer exponents 2-8 look for a pattern in integer exponents...
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Pre-Algebra
2-8 Look for a Pattern in Integer Exponents
2-8 Look for a Pattern in Integer Exponents
Pre-Algebra
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
2-8 Look for a Pattern in Integer Exponents
107
104
Warm UpEvaluate.
10001. 103
2. 100
3. 102 • 102
1
10,000
10004.
5. 106
1061
Pre-Algebra
2-8 Look for a Pattern in Integer Exponents
Pre-Algebra
2-8 Look for a Pattern in Integer Exponents
Problem of the Day
Find two different numbers for the values of x and y that will make xy and yx equal. 2 and 4
Pre-Algebra
2-8 Look for a Pattern in Integer Exponents
Learn to evaluate expressions with negative exponents.
Pre-Algebra
2-8 Look for a Pattern in Integer Exponents
Look for a pattern in the table to extend what you know about exponents to include negative exponents. Start with what you know about positive and zero exponents.
÷ 10 ÷ 10 ÷ 10 ÷ 10
102 101 100 10–1 10–2
10 • 10
100
10
10 1
1 110
110
= 0.1
110 • 10
1100
= 0.01
Pre-Algebra
2-8 Look for a Pattern in Integer Exponents
Additional Example 1A & 1B: Using a Pattern to Evaluate Negative Exponents
Evaluate the powers of 10.
A. 10–2
10–2 = 1
10 • 10
10–2 = 1100
= 0.01
B. 10–1
10 = = 0.1–1 110
10 =
–1 110
Pre-Algebra
2-8 Look for a Pattern in Integer Exponents
10–6 = = 0.0000011
1,000,000
Evaluate the powers of 10.
C. 10–6
10–6 = 1
10 • 10 • 10 • 10 • 10 • 10
Additional Example 1C: Using a Pattern to Evaluate Negative Exponents Continued
Pre-Algebra
2-8 Look for a Pattern in Integer Exponents
Try This: Example 1A & 1B
Evaluate the powers of 10.
A. 10–8
B. 10–9
10–8 = = 0.000000011
100,000,000
10–8 = 1
10 • 10 • 10 • 10 • 10 • 10 • 10 • 10
10–9 = = 0.00000000111,000,000,000
10–9 =1
10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10
Pre-Algebra
2-8 Look for a Pattern in Integer Exponents
10–7 = = 0.00000011
10,000,000
Evaluate the powers of 10.
C. 10–7
10–7 = 1
10 • 10 • 10 • 10 • 10 • 10 • 10
Try This: Example 1C
Pre-Algebra
2-8 Look for a Pattern in Integer Exponents
NEGATIVE EXPONENTS
Words Numbers Algebra
A power with a negative exponent equals 1 divided by that power with its opposite exponent.
b–n =1bn5–3 = =
1125
153
The reciprocal of a number is 1 divided by that number.
Remember!
Pre-Algebra
2-8 Look for a Pattern in Integer Exponents
5–3
Write the reciprocal; change the sign of the exponent.
15 • 5 • 5
1251
51
3
Additional Example 2: Evaluating Negative Exponents
Evaluate.
Pre-Algebra
2-8 Look for a Pattern in Integer Exponents
(–10)–3
Write the reciprocal; change the sign of the exponent.
Evaluate.
1–103
1(–10)(–10)(–10)
1 1000
–
Try This: Example 2
= –0.001
Pre-Algebra
2-8 Look for a Pattern in Integer Exponents
Bases are the same, so add the exponents.
A. 2–5 • 23
2 –5+3
2 –2
22
1 Write the reciprocal; change the sign of the exponent.
1 4
2 • 2 • 2 • 2 • 22 • 2 • 2= 1
4=
Additional Example 3A: Evaluating Products and Quotients of Negative Exponents
Evaluate.
Check: 2 • 23 = • 23 = 2 5 1 –5
2 23
5
Pre-Algebra
2-8 Look for a Pattern in Integer Exponents
Bases are the same, so subtract the exponents.
6
5–8
6
–3
163
Write the reciprocal; change the sign of the exponent.
65 68
2161
Check: 6
5 6 8 6 •6 • 6 • 6 • 6 • 6 • 6 •
6
6 •6 • 6 • 6 • 6=
Evaluate.
B.
=2161
Additional Example 3B: Evaluating Products and Quotients of Negative Exponents Continued
Pre-Algebra
2-8 Look for a Pattern in Integer Exponents
= 53
52
5 •5 • 55 • 5Check:
Bases are the same, so subtract the exponents.
5
2–3
5
–1
1 5 1
Write the reciprocal; change the sign of the exponent.
52 53
Evaluate.
15 5
1=
Try This: Example 3A
A.
Pre-Algebra
2-8 Look for a Pattern in Integer Exponents
Bases are the same, so add the exponents.
7
–6+7
7
1
7
Evaluate.
B. 7–6 • 77
Try This: Example 3B
7 • 7 = = Check: 7–6 176 • 7 7 7 7
67
= 7 • 7 • 7 • 7 • 7 • 7 • 7
7 • 7 • 7 • 7 • 7 • 7 = = 7 71
Pre-Algebra
2-8 Look for a Pattern in Integer Exponents
Lesson Quiz: Part 1
Evaluate the powers of 10.
1. 10–3 0.001
2. 10–7 0.0000001
Evaluate.
3. (–6)–2 361
4. 74 •7–4 1
5. 729
192 95
Pre-Algebra
2-8 Look for a Pattern in Integer Exponents
6. In engineering notation, a tera is equal to 1012, and a mega is equal to 106. How many megas are equal to a tera?
Lesson Quiz: Part 2
106