1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Warm Up
Evaluate.
1. 103
1000
2. 101 1
3. 104
10,000
4. 105
100,000
5. 106
1,000,000

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. Sunshine State Standards
Prep for MA.8.A.6.1 Use exponents…to write large and small numbers and vice versa and to solve problems.
Also MA.8.A.6.4

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.

6. Additional Example 1: Using a Pattern to Simplify Negative Exponents
Simplify. Write in decimal form.
A. 10–2
10–2 = 1
10 • 10
Extend the pattern from the table. = 1
100
= 0.01
Multiply. Write as a decimal.
B. 10–1
Extend the pattern from the table. = 1 10
= 0.1
Write as a decimal.

7. 10–8 = Check It Out: Example 1A Simplify. Write in decimal form. 10–8
100,000,000
10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 =
10–8

8. 10–5 = Check It Out: Example 1B 10–5 10 • 10 • 10 • 10 • 10 1 100,000=
10–5

9. NEGATIVE EXPONENTS

10. Additional Example 2A: Evaluating Negative Exponents
Simplify.
5–3
Write the power under 1; change the sign of the exponent.
Find the product.
Simplify.

11. Additional Example 2B: Evaluating Negative Exponents
Simplify.
(–10)–3
Write the power under 1; change the sign of the exponent. 1
–10 • –10 • –10
Find the product.
–1000 1
= –0.001
Simplify.

12. (–3)5 1 Check It Out: Example 2A Simplify. (–3)–5 = or – –243
(–3) • (–3) • (–3) • (–3) • (–3)
(–3)–5
243

13. (–4) • (–4) • (–4) • (–4) • (–4) • (–4)
Check It Out: Example 2B
Simplify.
(–4)–6
4096 1
(–4)6
(–4) • (–4) • (–4) • (–4) • (–4) • (–4)
(–4)–6 =

15. Additional Example 3: Using the Order of Operations
Evaluate 5 – (6 – 4)–3 + (– 2)0.
5 – (6 – 4)–3 + (–2)0
= 5 – (2)–3 + (–2)0
Subtract inside the parentheses.
= 5 –
1 8
Evaluate the exponents.
= 5
7 8
Add and subtract from left to right.

16. Check It Out: Example 3A
Simplify 10 + (5 + 3)– +
10 + 8–2 + 1 = 11
1 82
= 11 +
1 64
= 11

17. Check It Out: Example 3B
Simplify (7 – 3)3 + 2–2 – 5.
43 + 2–2 – 5 = 64
= 59
1 4 +
1 22
= 64 +
– 5
= 59 +

18. Lesson Quiz for Student Response Systems
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems 18

19. Lesson Quiz
Evaluate the powers of 10.
1. 10–3
0.001
2. 10–7
Evaluate.
3. (–6)–2
4. 4 • 2–3 +10–1
5. 80 –(11 – 24)–2
6. (4w)–2 + w–1 for w = 4

20. Lesson Quiz for Student Response Systems
1. Evaluate 10–4.
A. –40 B C D 20

21. Lesson Quiz for Student Response Systems
2. Evaluate 2–4.
A. –8
B. 8
C. 16 D. 21

22. Lesson Quiz for Student Response Systems
3. Evaluate 82 –(11 – 20)–2.
A. –8
B. 62
C. 64
D. 156 22