1. 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

2. 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.

3. 10–8 10–8 = = Multiply. Write as a decimal. Check It Out! Example 1A
Simplify the powers of 10.
10–8
10–8 = 1
10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 = 1
100,000,000
Multiply. =
Write as a decimal.

4. 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.

5. NEGATIVE EXPONENTS

6. 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.

7. 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.

8. 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.

9. 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.

11. 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.