1. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 5.6 Rules of Exponents and Scientific Notation

2. Copyright 2013, 2010, 2007, Pearson, Education, Inc. What You Will Learn Exponents Rules of Exponents Scientific Notation 5.6-2

3. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Exponents Given 5 2, 2 is the exponent, 5 is the base Read 5 2 as “5 to the second power” or “5 squared,” which means 5.6-3

4. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Exponents “5 to the third power,” or “5 cubed” is “b to the nth power,” or b n, means mulitiply b n times. 5.6-4

5. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 1: Evaluating the Power of a Number Evaluate. a)5 2 = 5 5= 25 b)(–3) 2 = (–3) (–3)= 9 c)3 4 = 3 3 3 3= 81 d)1 1000 = 1 e)1000 1 = 1000 5.6-5

6. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 2: The Importance of Parentheses Evaluate. a)(–2) 4 = (–2)(–2)(–2)(–2) = 4(–2)(–2) b)–2 4 = –1 2 4 = –1 2 2 2 2 =–8(–2) = 16 = –1 16 = –16 5.6-6

7. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Product Rule for Exponents 5.6-7

8. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 3: Using the Product Rule for Exponents Use the product rule to simplify. a)3 3 3 2 = 3 3+2 = 3 5 b)5 5 3 = 5 1 5 3 = 5 1+3 =243 = 5 4 = 625 5.6-8

9. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Quotient Rule for Exponents 5.6-9

10. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 4: Using the Quotient Rule for Exponents Use the quotient rule to simplify. = 3 7–5 = 3 2 = 5 9–5 =9=9 = 5 4 = 625 5.6-10

11. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Zero Exponent Rule 5.6-11

12. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 5: The Zero Power Use the zero exponent rule to simplify. Assume x ≠ 0. a)2 0 = 1 b) (–2) 0 c)–2 0 = –1 2 0 = –1 1 = 1 = –1 d) (5x) 0 = 1 e) 5x 0 = 5 x 0 = 5 1= 5 5.6-12

13. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Negative Exponent Rule 5.6-13

14. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 6: Using the Negative Exponent Rule Use the negative exponent rule to simplify. 5.6-14

15. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Power Rule for Exponents 5.6-15

16. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 7: Evaluating a Power Raised to Another Power Use the power rule to simplify. a) (5 4 ) 3 = 5 12 = 5 4 3 b) (7 2 ) 5 = 7 10 = 7 2 5 5.6-16

17. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Rules for Exponents Product Rule Quotient Rule Zero Exponent Rule Negative Exponent Rule Power Rule 5.6-17

18. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Scientific Notation Many scientific problems deal with very large or very small numbers. Distance from the Earth to the sun is 93,000,000,000,000 miles. Wavelength of a yellow color of light is 0.0000006 meter. 5.6-18

19. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Scientific notation is a shorthand method used to write these numbers. 93,000,000 = 9.3 × 10,000,000 = 9.3 × 10 7 0.0000006 = 6.0 × 0.0000001 = 6.0 × 10 –7 Scientific Notation 5.6-19

20. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 8: Converting from Decimal Notation to Scientific Notation Write each number in scientific notation. a) In 2010, the population of the United State was about 309,500,000. 309,500,000 = 3.095 × 10 8 b) In 2010, the population of the China was about 1,348,000,000. 1,348,000,000 = 1.348 × 10 9 5.6-20

21. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 8: Converting from Decimal Notation to Scientific Notation c) In 2010, the population of the world was about 6,828,000,000. 6,828,000,000 = 6.828 × 10 9 d) The diameter of a hydrogen atom nucleus is about 0.0000000000011 millimeter. 0.0000000000011 = 1.1 × 10 –12 5.6-21

22. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 8: Converting from Decimal Notation to Scientific Notation e) The wavelength of an x-ray is about 0.000000000492. 0.000000000492 = 4.92 × 10 –10 5.6-22

23. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 9: Converting from Scientific Notation to Decimal Notation Write each number in decimal notation. a) The average distance from Mars to the sun is about 1.4 × 10 8 miles. 1.4 × 10 8 = 140,000,000 b) The half-life of uranium-235 is about 4.5 × 10 9 years. 4.5 × 10 9 = 4,500,000,000 5.6-23

24. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 9: Converting from Scientific Notation to Decimal Notation c) The average grain size in siltstone is about 1.35 × 10 –3 inch. 1.35 × 10 –3 = 0.00135 d) A millimicron is a unit of measure used for very small distances. One millimicron is about 3.94 × 10 –8 inch. 3.94 × 10 –8 = 0.0000000394 5.6-24

25. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 10: Multiplying Numbers in Scientific Notation Multiply (2.1 × 10 5 )(9 × 10 –3 ). Write the answer in scientific notation and in decimal notation. (2.1 × 10 5 )(9 × 10 –3 ) = (2.1 × 9)(10 5 × 10 –3 ) = 18.9 × 10 2 = 1890 5.6-25

26. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 11: Dividing Numbers in Scientific Notation Divide. Write the answer in scientific notation and in decimal notation. 5.6-26

27. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 11: Dividing Numbers in Scientific Notation Solution 5.6-27