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Preview Warm Up California Standards Lesson Presentation

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

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**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

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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

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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

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**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.

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**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.

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**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.

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NEGATIVE EXPONENTS

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**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.

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**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.

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**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.

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**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.

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**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.

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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.

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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.

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