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Exponents and Negative Powers: Simplifying and Evaluating

Learn how to simplify expressions with negative exponents and evaluate powers with zero exponent. Find patterns and extend your knowledge to include negative exponents. Practice with quizzes.

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Exponents and Negative Powers: Simplifying and Evaluating

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  1. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

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

  3. Problem of the Day Find two different numbers for the values of x and y that will make xy and yx equal. 2 and 4

  4. Learn to simplify expressions with negative exponents and to evaluate the zero exponent.

  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 ÷ 10 ÷ 10 ÷ 10 ÷ 10 Look for a pattern in the table to extend what you know about exponents to include negative exponents.

  6. 1 10–2 = 10 • 10 1 = 0.01 = 100 1 = 10 1 = = 0.1 10 Additional Example 1: Using a Pattern to Simplify Negative Exponents Simplify. Write in decimal form. A. 10–2 Extend the pattern from the table. Multiply. Write as a decimal. B. 10–1 Extend the pattern from the table. Multiply. Write as a decimal.

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

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

  9. 1 5 Find the product of three ’s. Additional Example 2A: Evaluating Negative Exponents Simplify. 5–3 Write the power under 1; change the sign of the exponent. Simplify.

  10. 1 –10 1 Find the product of three ’s. –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

  11. 2 1 4 1 4 1 Find the product of two ’s. 4 • 4 1 16 Check It Out: Example 2A Simplify. 4–2 Write the reciprocal; change the sign of the exponent. Simplify.

  12. 1 4 –7 1 –7 1 Find the product of four ’s. –7 • –7 • –7 • –7 1 2401 Check It Out: Example 2B Simplfy. (–7)–4 Write the reciprocal; change the sign of the exponent. Simplify.

  13. 1 8 = 5 – + 1 7 8 = 5 Additional Example 3: Using the Order of Operations Evaluate 5 – (6 – 4)–3+ (–2)0. 5 – (6 – 4)–3+ (–2)0 = 5 – (2)–3+ (–2)0 Subtract inside the parentheses. Evaluate the exponents. Add and subtract from left to right.

  14. 1 9 = 3 + + 1 1 9 = 4 Check It Out: Example 3 Evaluate 3 + (7 – 4)–2+ (–8)0. 3 + (7 – 4)–2+ (–8)0 = 3 + (3)–2+ (–8)0 Subtract inside the parentheses. Evaluate the exponents. Add.

  15. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

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

  17. Lesson Quiz for Student Response Systems 1. Evaluate 10–4. A. –40 B. 0.001 C. 0.0001 D. 0.00001

  18. Lesson Quiz for Student Response Systems 2. Evaluate 2–4. A. –8 B. 8 C. 16 D.

  19. Lesson Quiz for Student Response Systems 3. Evaluate 82 –(11 – 20)–2. A. –8 B. 62 C. 64 D. 156

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