1. Preview
Warm Up
California Standards
Lesson Presentation

2. Warm Up
Simplify.
1000 10
10,000 4.
105
100,000 5.
106
1,000,000

3. NS2. 1 Understand negative whole-number exponents
NS2.1 Understand negative whole-number exponents. Multiply and divide expressions involving exponents with a common base.
AF2.1 Interpret positive whole-number powers as repeated multiplication and negative whole-number powers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate expressions that include exponents.
California
Standards

4. Look at the pattern shown in the table to extend what you know about exponents to include negative exponents. 10 2 1 –1 –2
10 • 10
100
= 0.1
= 0.01
÷ 10
÷ 10
÷ 10
÷ 10

5. Notice from the chart that as the exponents decrease by 1, the value of the expression decreases by a factor of 10. 10 2 1 –1 –2
10 • 10
100
= 0.1
= 0.01
÷ 10
÷ 10
÷ 10
÷ 10

6. Additional Example 1: Using a Pattern to Evaluate Negative Exponents
Simplify the powers of 10.
A. 10–2
10–2 = 1
10 • 10 = 1
100
= 0.01
Multiply. Write as a decimal.
B. 10–1
10 = –1 1 10
= = 0.1 1 10
Multiply. Write as a decimal.

7. Extend the pattern from the table.
Check It Out! Example 1A
Simplify the powers of 10.
10–8
Extend the pattern from the table.
10–8 = 1
10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 = 1
100,000,000
Multiply. =
Write as a decimal.

8. Extend the pattern from Example 1A.
Check It Out! Example 1B
Simplify the powers of 10.
10–9
Extend the pattern from Example 1A.
10–9 = 1
10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 = 1
1,000,000,000
Multiply. =
Write as a decimal.

9. NEGATIVE EXPONENTS

10. Additional Example 2A: Evaluating Negative Exponents
Simplify.
5–3
Write the power under 1; change the sign of the exponent. 1
5 • 5 • 5 =
Find the product.
125 1 =
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. Simplify. 4–2 Check It Out! Example 2A
Write the power under 1; change the sign of the exponent. 1
4 • 4 =
Find the product. 16 1 =
Simplify.

13. Simplify. (–7)–4 Check It Out! Example 2B
Write the power under 1; change the sign of the exponent. 1
–7 • –7 • –7 • –7 =
Find the product.
2401 1 =
Simplify.

15. Additional Example 3: Using the Order of Operations
Simplify 5 – (6 – 4)–3 + (–2)0.
5 – (6 – 4)–3 + (–2)0
5 – (2)–3 + (–2)0
Subtract inside the parentheses.
5 –
1 23
Rewrite 2-3.
5 –
1 8
Simplify the powers. 5
7 8
Add and subtract from left to right.

16. Check It Out! Example 3
Simplify 3 + (7 – 4)–2 + (–8)0.
3 + (7 – 4)–2 + (–8)0
3 + (3)–2 + (–8)0
Subtract inside the parentheses.
(–8)0
1 32
Rewrite 3-2.
1 9
Simplify the powers. 4
1 9
Add.

17. Lesson Quiz
Simplify the powers of 10.
1. 10–3
0.001
2. 10–7
Simplify.
1 36
3. (–6)–2
4. 4 • 2–3 + 10–1
5. 80 – (11 – 24)–2
6. Evaluate (4w)–2 + w–1 for w = 4.