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Exponents: Multiply and Divide Powers

Learn how to simplify real number expressions using the laws of exponents and how to multiply and divide powers with the same base. Includes quizzes.

rshoemaker
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Exponents: Multiply and Divide Powers

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

  2. Warm Up Evaluate. 27 1. 33 2. 4 • 4 • 4 • 4 256 3.b2 for b = 4 16 4. n2r for n = 3 and r = 2 18

  3. Problem of the Day Calculate 6 to the fourth power minus 56. 1240

  4. Sunshine State Standards Prep for MA.8.A.6.3 Simplify real number expressions using the laws of exponents. Also MA.8.A.6.4

  5. The factors of a power, such as 74, can be grouped in different ways. Notice the relationship of the exponents in each product. 7 • 7 • 7 • 7 = 74 (7 • 7 • 7) • 7 = 73 • 71 = 74 (7 • 7) • (7 • 7) = 72 • 72 = 74

  6. A. 66 •63 6 6+ 3 6 9 n 5 + 7 n 12 Additional Example 1: Multiplying Powers with the Same Base Multiply. Write the product as one power. Add exponents. B. n5 •n7 Add exponents.

  7. 1 2 Think: 2 = 2 5 + 1 2 6 24 4 + 4 24 8 Additional Example 1: Multiplying Powers with the Same Base Continued Multiply. Write the product as one power. C. 25 • 2 Add exponents. D.244• 244 Add exponents.

  8. A. 42 •44 4 2 + 4 6 = 4 x 4 + 2 = x 6 Check It Out: Example 1 Multiply. Write the product as one power. 42• 44 = B. x4 •x2 x4•x2 =

  9. 1 + 2 2 + 2 15 p Check It Out: Example 1 Continued Multiply. Write the product as one power. C. 15• 152 151• 152 = = 153 D. p2• p2 p2•p2 = = p4

  10. 5555 5 5555 5 5 5 = = = 5 5 = 52 555 555 53 Notice what occurs when you divide powers with the same base.

  11. 5 7 3 7 5 – 3 7 2 7 10 x 9 x 10 – 9 x Think: x = x 1 Additional Example 2: Dividing Powers with the Same Base Divide. Write the quotient as one power. A. Subtract exponents. B. Subtract exponents. x

  12. 9 – 2 =9 8 – 5 3 = n = n Check It Out: Example 2 Divide. Write the quotient as one power. 9 9 A. 9 2 9 9 = 97 9 2 n 8 B. n 5 n 8 n 5

  13. Reading Math 5 4 (9 ) is read as “nine to the fourth, to the fifth.” RAISING A POWER TO A POWER

  14. Additional Example 3: Raising a Power to a Power Simplify. A. (54)2 (54)2 54 • 2 Multiply exponents. 58 B. (67)9 (67)9 Multiply exponents. 67 • 9 663

  15. 12 –3 2 3 12 • –3 2 3 Additional Example 3: Raising a Power to a Power Simplify. D. (172)–20 C. (172)–20 Multiply exponents. Multiply exponents. 172 • –20 17–40

  16. Check It Out: Example 3 Simplify. A. (72)–1 (72)–1 1 72 • –1 = 7–2 = 49 B. (7–1)2 (7–1)2 1 7–1 • 2 = 7–2 = 49

  17. 4 4 –2 –2 1 5 1 5 –8 4 • –2 1 5 1 5 Check It Out: Example 3 Continued Simplify. D. (5–2)–3 C. (5–2)–3 = 5–2• –3 = 56 = = 15,625 = =58 = 390,625

  18. Additional Example 4: Application The speed of sound at sea level is 3.4029 x 102 meters per second. A ship that is 5 kilometers offshore sounds its horn. About how many seconds will pass before a person standing on shore will hear the sound? Write your answer in scientific notation.

  19. Additional Example 4 Continued distance = rate x time 5 km = (3.4029 x 102) x t Write 5 km as meters. 5000 = (3.4029 x 102) x t 5 x 103 = (3.4029 x 102) x t Write 5000 in scientific notation. 3.4029 x 102 3.4029 x 102 5 103 x = t 3.4029 x 102 102 1.469 x 101  t It would take about 1.5 x 101 seconds for the sound to reach the shore.

  20. Check It Out: Example 4 The diameter of a red blood cell is about 7.6 × 10-4 millimeters. Thai has a slide with a 2-cm drop of red blood cells on it. Approximately how many cells are on the slide? Write your answer in scientific notation. (Hint: Find the ratio of the size of the drop, in millimeters, to the size of one cell.)

  21. Check It Out: Example 4 Continued size of drop = number of red blood cells in drop; size of red blood cell 2 x 101 2 mm 2 cm = = 7.6 x 10–4 7.6 x 10–4 mm 7.6 x 10–4 mm 2 7.6 101 10–4 x = ≈ 0.2632 x 105 = 2.632 x 104 cells

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

  23. n 8 7 9 t9 109 4 t 2 10 t7 105 3 10 Lesson Quiz Write the product or quotient as one power. 1. n3n4 2. 8 • 88 4. 3. 6. (m2)19 m38 5. 32 • 33 • 35 8. (104)0 1 7. (9-8)9 9–72

  24. Lesson Quiz for Student Response Systems 1. Write the product as one power. d4 d3 A. d7 B. d12 C. 7d D. 12d

  25. Lesson Quiz for Student Response Systems 2. Write the product as one power. 44 43  42 A. 49 B. 414 C.424 D.4432

  26. Lesson Quiz for Student Response Systems 3. Write the product as one power. (10–1)0 A. 10–10 B. 0 C.1 D.10

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