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Notes 56

Notes 56. Integer Exponents. –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.

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Notes 56

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  1. Notes 56 Integer Exponents

  2. –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.

  3. 1 10–2 = 10 • 10 1 = 0.01 = 100 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. Write as a decimal. = 0.1

  4. Check It Out: Example 1A Simplify. Write in decimal form. 10–8

  5. Check It Out: Example 1B 10–5

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

  7. 1 –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. Find the product. Simplify. = –0.001

  8. Check It Out: Example 2A Simplify. (–3)–5

  9. Check It Out: Example 2B Simplify. (–4)–6

  10. 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.

  11. Check It Out: Example 3A Simplify 10 + (5 + 3)–2+ 50.

  12. Check It Out: Example 3B Simplify (7 – 3)3+ 2–2 – 5.

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