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Look for a Pattern in Integer Exponents

Look for a Pattern in Integer Exponents. 10 7. 10 6. 10 4. 10 6. Warm Up. Evaluate. 1000. 1. 10 3. 1. 2. 10 0. 10,000. 3. 10 2 • 10 2. 4. 1000. 5. 1. Learn to evaluate expressions with negative exponents. –2. 0. –1. 2. 1. 10. 10. 10. 10. 10. 1. 1. 10 • 10.

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Look for a Pattern in Integer Exponents

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  1. Look for a Pattern in Integer Exponents

  2. 107 106 104 106 Warm Up Evaluate. 1000 1. 103 1 2. 100 10,000 3. 102 • 102 4. 1000 5. 1

  3. Learn to evaluate expressions with negative 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 ÷10 ÷10 ÷10 ÷10 Look for a pattern in the table to extend what you know about exponents to include negative exponents. Start with what you know about positive and zero exponents.

  5. 1 1 –1 10 = 10–2 = 10 10 • 10 1 –1 10 = = 0.1 1 10 = 0.01 10–2 = 100 Example: Using a Pattern to Evaluate Negative Exponents Evaluate the powers of 10. A. 10–2 B. 10–1

  6. 1 10–6 = 10 • 10 • 10 • 10 • 10 • 10 1 10–6 = = 0.000001 1,000,000 Example: Using a Pattern to Evaluate Negative Exponents Continued Evaluate the powers of 10. C. 10–6

  7. 1 10–8 = 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 1 10–8 = = 0.00000001 100,000,000 1 10–9 = 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 1 10–9 = = 0.000000001 1,000,000,000 Try This Evaluate the powers of 10. A. 10–8 B. 10–9

  8. 1 10–7 = 10 • 10 • 10 • 10 • 10 • 10 • 10 1 10–7 = = 0.0000001 10,000,000 Try This Evaluate the powers of 10. C. 10–7

  9. 5–3 = = 1 53 1 1 b–n = bn 125 Remember! The reciprocal of a number is 1 divided by that number. NEGATIVE EXPONENTS Words Numbers Algebra A power with a negative exponent equals 1 divided by that power with it’s opposite exponent.

  10. 1 1 5 3 5 • 5 • 5 1 125 Example: Evaluating Negative Exponents Evaluate. 5–3 Write the reciprocal; change the sign of the exponent.

  11. 1 –103 1 (–10)(–10)(–10) 1 – 1000 Try This Evaluate. (–10)–3 Write the reciprocal; change the sign of the exponent. = –0.001

  12. –5+3 2 –2 2 1 22 1 1 23 Check: 2 • 23 = • 23 = –5 2 5 2 5 4 1 2 • 2 • 2 = = 4 2 • 2 • 2 • 2 • 2 Example: Evaluating Products and Quotients of Negative Exponents Evaluate. A. 2–5• 23 Bases are the same, so add the exponents. Write the reciprocal; change the sign of the exponent.

  13. 65 68 6 5–8 6 –3 1 63 1 6 5 1 6 •6 • 6 • 6 • 6 Check: = = 216 216 6 •6 • 6 • 6 • 6 • 6 • 6 • 6 6 8 Example: Evaluating Products and Quotients of Negative Exponents Continued Evaluate. B. Bases are the same, so subtract the exponents. Write the reciprocal; change the sign of the exponent.

  14. 52 53 5 2–3 5 –1 1 1 5 1 52 5 • 5 = Check: 5 1 5 53 5 •5 • 5 = Try This Evaluate. A. Bases are the same, so subtract the exponents. Write the reciprocal; change the sign of the exponent.

  15. 7 –6+7 1 7 7 7 1 Check: –6 7 • 7 7 7 • 7 = = 7 • 7 • 7 • 7 • 7 • 7 • 7 7 7 7 6 6 = = = 7 1 7 • 7 • 7 • 7 • 7 • 7 Try This Evaluate. B. 7–6 •77 Bases are the same, so add the exponents. 7

  16. 1 1 36 729 92 95 Lesson Quiz: Part 1 Evaluate the powers of 10. 0.001 1. 10–3 0.0000001 2. 10–7 Evaluate. 3. (–6)–2 1 4. 74 •7–4 5.

  17. 6 10 Lesson Quiz: Part 2 6. In engineering notation, a tera is equal to 1012, and a mega is equal to 106. How many megas are equal to a tera?

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