1. 2-8 Warm Up Problem of the Day Lesson Presentation
Look for a Pattern in
Integer Exponents
2-8
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra

2. Pre-Algebra
2-8
Look for a Pattern
in Integer Exponents
Warm Up
Evaluate.
1000 1
• 102
10,000
107
104 4.
1000
106 5. 1

3. 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

4. Learn to evaluate expressions with negative exponents.

5. 10 2 1 –1 –2
10 • 10
100
= 0.1
= 0.01
÷ 10
÷ 10
÷ 10
÷ 10
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.

6. Evaluate the powers of 10. A. 10–2 10–2 = 10–2 = = 0.01 B. 10–1 10 =
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 = 1
100
= 0.01
B. 10–1
10 = –1 1 10
10 = = 0.1 –1 1 10

7. Additional Example 1C: Using a Pattern to Evaluate Negative Exponents Continued
Evaluate the powers of 10.
C. 10–6
10–6 = 1
10 • 10 • 10 • 10 • 10 • 10
10–6 = = 1
1,000,000

8. Try This: Example 1A & 1B
Evaluate the powers of 10.
A. 10–8
10–8 = 1
10 • 10 • 10 • 10 • 10 • 10 • 10 • 10
10–8 = = 1
100,000,000
B. 10–9
10–9 = 1
10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10
10–9 = = 1
1,000,000,000

9. C. 10–7 10–7 = 10–7 = = 0.0000001 Try This: Example 1C
Evaluate the powers of 10.
C. 10–7
10–7 = 1
10 • 10 • 10 • 10 • 10 • 10 • 10
10–7 = = 1
10,000,000

10. NEGATIVE EXPONENTS Words Numbers Algebra 5–3 = = 125 53 b–n = bn
A power with a negative exponent equals 1 divided by that power with its opposite exponent.
5–3 = = 1
125 53
b–n = 1 bn
The reciprocal of a number is 1 divided by that number.
Remember!

11. Additional Example 2: Evaluating Negative Exponents
Evaluate.
5–3 5 1 3
Write the reciprocal; change the sign of the exponent. 1
5 • 5 • 5
125 1

12. Try This: Example 2
Evaluate.
(–10)–3 1
–103
Write the reciprocal; change the sign of the exponent. 1
(–10)(–10)(–10) 1
1000 –
= –0.001

13. Additional Example 3A: Evaluating Products and Quotients of Negative Exponents
Evaluate.
A. 2–5 • 23 2
–5+3
Bases are the same, so add the exponents. 2 –2 22 1
Write the reciprocal; change the sign of the exponent. 1 4
Check: 2 • 23 = • 23 = 2 5 1 –5 23 1 4 =
2 • 2 • 2 • 2 • 2
2 • 2 • 2 =

14. Evaluate. B. 65 68 Bases are the same, so subtract the exponents. 6 6
Additional Example 3B: Evaluating Products and Quotients of Negative Exponents Continued
Evaluate. 65 68 B.
Bases are the same, so subtract the exponents. 6
5–8 6 –3 1 63
Write the reciprocal; change the sign of the exponent.
216 1
Check: 6 5 8
6 • 6 • 6 • 6 • 6 • 6 • 6 • 6
6 • 6 • 6 • 6 • 6 = =
216 1

15. Try This: Example 3A
Evaluate. 52 53 A.
Bases are the same, so subtract the exponents. 5
2–3 5 –1 1 5
Write the reciprocal; change the sign of the exponent. 1 5 = 53 52
5 • 5 • 5
5 • 5
Check: 5 1 =

16. Evaluate. Check: B. 7–6 • 77 Bases are the same, so add the exponents.
Try This: Example 3B
Evaluate.
B. 7–6 • 77 7
–6+7
Bases are the same, so add the exponents. 7 1
7 • 7 = =
Check: 7 –6 1 6
• 7 7 =
7 • 7 • 7 • 7 • 7 • 7 • 7
7 • 7 • 7 • 7 • 7 • 7
= = 7 7 1

17. Evaluate the powers of 10. 1. 10–3 0.001 2. 10–7 0.0000001 Evaluate.
Lesson Quiz: Part 1
Evaluate the powers of 10.
1. 10–3
0.001
2. 10–7
Evaluate. 36 1
3. (–6)–2
• 7–4 1 5.
92 95
729 1

18. Lesson Quiz: Part 2
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? 10 6