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

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

4. 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.

5. Example 1: Using a Pattern to Simplify Negative Exponents
Simplify. Write in decimal form.
A. 10–2
B. 10–1
10–2 = 1
10 • 10 = 1 10 = 1
100
= 0.01
= = 0.1 1 10

6. = 10–8 = Check It Out: Example 1A Simplify. Write in decimal form. 1
10 • 10 • 10 • 10 • 10 • 10 • 10 • 10
10–8 = 1
100,000,000 =

7. 10–9 = = Check It Out: Example 1B 1
10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10
10–9 = 1
1,000,000,000 =

9. Example 2: Evaluating Negative Exponents
Simplify.
A. 5–3
B. (–10)–3 1
–10 • –10 • –10
–1000 1
= –0.001

10. Simplify. A. 4–2 B. (–7)–4 4 1 Check It Out: Example 2 1 –7 1 1 4 • 4
–7 • –7 • –7 • –7 16 1
2401 1

12. 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
= 5 –
1 8
= 5
7 8

13. Check It Out: Example 3
Evaluate 3 + (7 – 4)–2 + (–8)0.
3 + (7 – 4)–2 + (–8)0
= 3 + (3)–2 + (–8)0 =
1 9
= 4
1 9

14. 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