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Unit 6 – Chapter 8

Unit 6 – Chapter 8. Unit 6. Chapter 7 Review and Chap. 8 Skills Section 8.1 – Exponent Properties with products Section 8.2 – Exponent Properties with quotients Section 8.3 – Define and Use Zero and Negative Exponents Section 8.4 – Use Scientific Notation

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Unit 6 – Chapter 8

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  1. Unit 6 – Chapter 8

  2. Unit 6 • Chapter 7 Review and Chap. 8 Skills • Section 8.1 – Exponent Properties with products • Section 8.2 – Exponent Properties with quotients • Section 8.3 – Define and Use Zero and Negative Exponents • Section 8.4 – Use Scientific Notation • Section 8.5 – Write and Graph Exponential Growth Functions • Section 8.6 – Write and Graph Exponential Decay Functions

  3. Warm-Up – Ch. 8

  4. (–1, –1) ANSWER Daily Homework Quiz For use after Lesson 7.1 2. Solve the linear system by graphing. 2x + y = – 3 – 6x + 3y = 3

  5. 3. A pet store sells angel fish for $6 each and clown loaches for $4 each . If the pet store sold 8 fish for $36, how many of each type of fish did it sell? Daily Homework Quiz For use after Lesson 7.1 ANSWER 2 angel fish and 6 clown loaches

  6. 1. –5x – y =12 3x – 5y = 4 ANSWER (–2, –2) 2. 2x + 9y = –4 x – 2y = 11 ANSWER (7, –2 ) Daily Homework Quiz For use after Lesson 7.2 Solve the linear system using substitution

  7. 1. –5x +y = 18 3x–y = –10 ANSWER (–4, –2) 2. 4x + 2y = 14 4x – 3y = –11 ANSWER (1, 5) 3. – 7x– 3y = 11 4x – 2y = 16 ANSWER (1, – 6) Daily Homework Quiz For use after Lesson 7.3 Solve the linear system using elimination.

  8. 4. A recreation center charges nonmembers$3to use the pool and$5to use the basketball courts. A personpays$42to use the recreation facilities12times. How many times did the person use the pool. ANSWER 9times Daily Homework Quiz For use after Lesson 7.4 (-4,-2)

  9. 3. A group of 12 students and 3 teachers pays $57 for admission to a primate research center. Another group of 14 students and 4 teachers pays $69. Find the cost of one student ticket. ANSWER $3.50 Daily Homework Quiz For use after Lesson 7.3

  10. 1. Write a system of inequalities for the shaded region. ANSWER x < 2, y > x +1 Daily Homework Quiz For use after Lesson 7.6

  11. ANSWER Exponent: 8, base: 13 ANSWER Power Prerequisite Skills VOCABULARY CHECK 1. Identify the exponent and the base in the expression 138. 2. Copy and complete: An expression that represents repeated multiplication of the same factor is called a(n) ? .

  12. ANSWER ANSWER 25 100 27 36 6. z3whenz = 5. r2when r = ANSWER ANSWER 1 5 1 2 8 6 Prerequisite Skills SKILLS CHECK Evaluate the expression. 4. a3whena = 3 3. x2whenx = 10

  13. ANSWER ANSWER 6.01, 6.12, 6.2 0.0098, 0.073, 0.101 ANSWER ANSWER ANSWER ANSWER 1.45 0.04 0.005 0.138 Prerequisite Skills SKILLS CHECK Order the numbers from least to greatest. 7. 6.12, 6.2, 6.01 8. 0.073, 0.101, 0.0098 Write the percent as a decimal. 9. 4% 10. 0.5% 12. 145% 11. 13.8%

  14. 13. Write a rule for the function. ANSWER f (x) = x + 2 Prerequisite Skills SKILLS CHECK

  15. Warm-Up – 8.1

  16. 81 ANSWER 36 -36 ANSWER ANSWER Lesson 8.1, For use with pages 488-494 Evaluate the expression. 1.x4whenx = 3 3. -a2whena = –6 2.a2whena = –6

  17. –125 ANSWER 64 in.3 ANSWER Lesson 8.1, For use with pages 488-494 Evaluate the expression. 3.m3whenm = –5 4. A food storage container is in the shape of a cube. What is the volume of the container if one side is 4 inches long? Use V = s3.

  18. Vocabulary – 8.1 • Power • Repeated multiplication • Exponent • How many times to multiply a quantity • Base • Quantity multiplied • Order of Magnitude • The “power of 10” nearest the number

  19. Activity • What is a2 * a3? • Expand it out and combine like terms. • Do you notice anything about the exponent? • Try x3 * x4. What do you get? See any patterns? • What is (x2)3? • Expand it and combine like terms. • What do you notice about the exponent? • Try (x3)3 • What do you get? Notice any patterns?

  20. Notes – 8.1 – Exponents with Products • Product of Powers Rule • To Multiply Exponents w/ SAME BASE(!) • ADD THE EXPONENTS • am * an = a (m+n) • Power of a Power Rule • To raise powers to a power w/SAME BASE(!) • MULTIPLY THE EXPONENTS • (am)n = a (m * n) • Order of Magnitude • Round number to nearest power of 10 • The exponent of 10 is the “order of magnitude”

  21. Examples 8.1

  22. 51 59 32 37 1. 2. = 5 59 = (– 7)2 (– 7)1 3. (– 7)2(– 7) 4. x2x6x = x2x6x1 for Example 1 GUIDED PRACTICE Simplify the expression. = 32 + 7 = 39 = 51 + 9 = 510 = (– 7)2+1 = (–7)3 = x2 + 6+ 1 = x9

  23. [(–6)2]5 a. b. (25)3 = (–6)2 5 = 253 (x2)4 [(y + 2)6]2 c. d. = x24 EXAMPLE 2 Use the power of a power property = 215 = (–6)10 = (y+ 2)6 2 = (y + 2)12 = x8

  24. [(–2)4]5 6. = (–2)4 5 5. (42)7 (n3)6 [(m + 1)5]4 7. 8. = (m + 1)5 4 = n36 for Example 2 GUIDED PRACTICE Simplify the expression. = 427 = 414 = (–2)20 = (m + 1)20 = n18

  25. (24 13)8 = ? 248 138 a. a. b. b. (9xy)2 = (9 x y)2 = 92x2y2 = 81x2y2 EXAMPLE 3 Use the power of a product property

  26. c. c. d. d. d. d. d. d. (–4)2z2 = 16z2 (–4z)2 = (–4 z)2 What is the order of magnitude of 99? 90,000 is closest to 100,000 = 105, so Order of magnitude is 5. 99 is closest to 100 = 102, so Order of magnitude is 2. – (42z2) = –16z2 – (4z)2 = – (4 z)2 = What is the order of magnitude of 90,000? EXAMPLE 3 Use the power of a product property

  27. (2x3)2x4 = 22 (x3)2x4 = 4 x6x4 (2x3)2x4 EXAMPLE 4 Use all three properties Simplify Power of a product property Power of a power property = 4x10 Product of powers property

  28. (42 12)2 = 422 122 9. (–3n)2 10. 11. (9m3n)4 = 94 (m3) 4n 4 = (–3 n)2 = (–3)2n2 = 9n2 = 6561 m12n4 for Examples 3, 4 and 5 GUIDED PRACTICE Simplify the expression. Power of a product property Product of powers property = 6561 m12n4 Power of a power property

  29. 12. = 5 54 (x2)4 = 5 625 x8 5 (5x2)4 for Examples 3, 4 and 5 GUIDED PRACTICE Power of a product property Power of a power property = 3125x8 Product of powers property

  30. EXAMPLE 5 Solve a real-world problem Bees In 2003 the U.S. Department of Agriculture (USDA) collected data on about 103 honeybee colonies. There are about 104 bees in an average colony during honey production season. About how many bees were in the USDA study?

  31. ANSWER The USDA studied about 107, or 10,000,000, bees. EXAMPLE 5 Solve a real-world problem SOLUTION To find the total number of bees, find the product of the number of colonies, 103, and the number of bees per colony, 104. 103•104 = 103+4 = 107

  32. Warm-Up – 8.2

  33. 1 1.q3whenq = 4 3 1 9 ANSWER 5 64 25 2.c2whenc = ANSWER Lesson 8.2, For use with pages 495-501 Evaluate the expression.

  34. (–5n2)2 10. = (–5)2 (n2)2 = 25n4 about 106or 1,000,000 ANSWER Lesson 8.2, For use with pages 495-501 Evaluate the expression. 3.A magazine had a circulation of 9364 in 2001. The circulation was about 125 times greater in 2006.Use order of magnitude to estimate the circulation in 2006.

  35. Vocabulary – 8.2 • No new vocab words!!

  36. Activity • What is a3 / a2? • Expand it out and cancel like terms. • Do you notice anything about the exponents? • Try x5/x2. What do you get? See any patterns? • What is (1/2)3? • Expand it and combine like terms. • What do you notice about the exponent? • Try (2/3)3 • What do you get? Notice any patterns?

  37. Notes – 8.2 –Exponents with quotients • Quotient of Powers Rule • To Divide Powers w/ SAME BASE(!) • SUBTRACT THE EXPONENTS • am / an = a (m-n) • Power of a Quotient Rule • To raise fractions to a power: • Raise numerator and denominator to the power • (a/b)m = am/bm

  38. Examples 8.2

  39. a. (– 3)9 b. (– 3)3 512 810 84 57 54 58 = c. 57 EXAMPLE 1 Use the quotient of powers property = 810– 4 = 86 = (– 3)9 – 3 = (– 3)6 = 512 – 7 = 55

  40. x6 d. x6 = x4 1 x4 EXAMPLE 1 Use the quotient of powers property = x6 – 4 = x2

  41. 1. (– 4)9 2. (– 4)2 97 611 65 92 94 93 92 3. = for Example 1 GUIDED PRACTICE Simplify the expression. = 611 – 5 = 66 = (– 4)9 – 2 = (– 4)7 = 97 – 2 = 95

  42. y8 y5 4. y8 = 1 y5 for Example 1 GUIDED PRACTICE = y8 – 5 = y3

  43. 3 a. = – 7 (– 7)2 49 x x2 x2 x 7 x3 2 2 x y y3 – = = = b. EXAMPLE 2 Use the power of quotient property

  44. 3 4x2 64x6 (4x2)3 a. = a8 5y 125y3 (5y)3 = 2b5 43 (x2)3 = 53y3 = 1 1 a10 a2 (a2)5 2a2 b5 2a2 1 b 5 b. = 2a2 b5 = a10 2a2b5 = EXAMPLE 3 Use properties of exponents Power of a quotient property Power of a product property Power of a power property Power of a quotient property Power of a power property Multiply fractions. Quotient of powers property

  45. x2 ( x2)2 4y (4y)2 2 5. = – 5 (–5)3 125 y y3 y3 3 3 – – = = = 6. = a2 a 5 b y b2 2 = 7. x4 x4 = = 42y2 16y2 for Examples 2 and 3 GUIDED PRACTICE Simplify the expression. Power of a quotient property Power of a product property Power of a power property

  46. 8 s3 23s3 t5 t5 8. = 27 t3 33t3 16 16 3t 16 = 8 s3 t5 3 = t5 2s 27 16t3 s3 t2 54 = for Examples 2 and 3 GUIDED PRACTICE Power of a quotient property Power of a power property Multiply fractions.

  47. To construct what is known as a fractal tree, begin with a single segment (the trunk) that is 1 unit long, as in Step 0. Add three shorter segments that are unit long to form the first set of branches, as in Step 1. Then continue adding sets of successively shorter branches so that each new set of branches is half the length of the previous set, as in Steps 2 and 3. 1 2 EXAMPLE 4 Solve a multi-step problem Fractal Tree

  48. a. Make a table showing the number of new branches at each step for Steps 1 - 4. Write the number of new branches as a power of 3. How many times greater is the number of new branches added at Step 5 than the number of new branches added at Step 2? b. EXAMPLE 4 Solve a multi-step problem

  49. b. The number of new branches added at Step 5 is 35. The number of new branches added at Step 2 is 32. So, the number of new branches added at Step 5 is = 33 = 27 times the number of new branches added at Step 2. 35 32 EXAMPLE 4 Solve a multi-step problem SOLUTION a.

  50. 9. FRACTAL TREE In Example 4, add a column to the table for the length of the new branches at each step. Write the length of the new branches as power of . What is the length of a new branch added at Step 9? 1 1 ( ) 2 9 = 9 1 units 512 for Example 4 GUIDED PRACTICE SOLUTION

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