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Warm Up

Preview. Warm Up. California Standards. Lesson Presentation. 10 5. 10 6. Warm Up Simplify. 1000. 1. 10 3. 2. 10 1. 10. 3. 10 4. 10,000. 4. 100,000. 1,000,000. 5. California Standards.

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Warm Up

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  1. Preview Warm Up California Standards Lesson Presentation

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

  3. California Standards 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.

  4. –2 0 –1 2 1 10 10 10 10 10 1 1 10 • 10 10 1 10 • 10 10 1 1 = 0.01 = 0.1 1 100 10 100 10 Look at the pattern shown in the table to extend what you know about exponents to include negative exponents. ÷ 10 ÷ 10 ÷ 10 ÷ 10

  5. –2 0 –1 2 1 10 10 10 10 10 1 1 10 • 10 10 1 10 • 10 10 1 1 = 0.01 = 0.1 1 100 10 100 10 Notice from the chart that as the exponents decrease by 1, the value of the expression decreases by a factor of 10. ÷ 10 ÷ 10 ÷ 10 ÷ 10

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

  7. 1 10–8 = 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 1 = 100,000,000 Check It Out! Example 1A Simplify the powers of 10. 10–8 Extend the pattern from the table. Multiply. Write as a decimal. = 0.00000001

  8. 1 10–9 = 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 1 = 1,000,000,000 Check It Out! Example 1B Simplify the powers of 10. 10–9 Extend the pattern from Example 1A. Multiply. Write as a decimal. = 0.000000001

  9. NEGATIVE EXPONENTS

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

  11. 1 Find the product. = –10 • –10 • –10 1 = –1000 Additional Example 2B: Evaluating Negative Exponents Simplify. (–10)–3 Write the power under 1; change the sign of the exponent. Simplify. = –0.001

  12. 1 Find the product. = 4 • 4 1 = 16 Check It Out! Example 2A Simplify. 4–2 Write the power under 1; change the sign of the exponent. Simplify.

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

  14. 1 23 1 8 7 8 5 5 – + 1 5 – + 1 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. Rewrite 2-3. Simplify the powers. Add and subtract from left to right.

  15. 1 9 1 32 1 9 4 3 + + 1 3 + + (–8)0 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. Rewrite 3-2. Simplify the powers. Add.

  16. Lesson Quiz Simplify the powers of 10. 0.001 1. 10–3 0.0000001 2. 10–7 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.

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