Preview Warm Up California Standards Lesson Presentation

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

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

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

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

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.

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. = 0.00000001 Write as a decimal.

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. = 0.000000001 Write as a decimal.

NEGATIVE EXPONENTS

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.

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.

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.

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.

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 1 23 Rewrite 2-3. 5 – + 1 1 8 Simplify the powers. 5 7 8 Add and subtract from left to right.

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. 3 + + (–8)0 1 32 Rewrite 3-2. 3 + + 1 1 9 Simplify the powers. 4 1 9 Add.

Lesson Quiz Simplify the powers of 10. 1. 10–3 0.001 2. 10–7 0.0000001 Simplify. 1 36 3. (–6)–2 3 5 4. 4 • 2–3 + 10–1 24 25 5. 80 – (11 – 24)–2 65 256 6. Evaluate (4w)–2 + w–1 for w = 4.