1. 4-4 Laws of Exponents Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. 4-4 Laws of Exponents Warm Up Evaluate. 27 1. 3 3 2. 4 4 4 4 3. b 2 for b = 4 4. n 2 r for n = 3 and r = 2 256 16 18

3. 4-4 Laws of Exponents Problem of the Day Calculate 6 to the fourth power minus 56. 1240

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

5. 4-4 Laws of Exponents The factors of a power, such as 7 4, can be grouped in different ways. Notice the relationship of the exponents in each product. 7 7 7 7 = 7 4 (7 7 7) 7 = 7 3 7 1 = 7 4 (7 7) (7 7) = 7 2 7 2 = 7 4

6. 4-4 Laws of Exponents

7. 4-4 Laws of Exponents Additional Example 1: Multiplying Powers with the Same Base A. 6 6 6 3 6 9 6 6 + 3 B. n 5 n 7 n 12 n 5 + 7 Add exponents. Multiply. Write the product as one power.

8. 4-4 Laws of Exponents D. 24 4 24 4 C. 2 5 2 2 6 2 5 + 1 24 8 4 + 4 Think: 2 = 2 1 Additional Example 1: Multiplying Powers with the Same Base Continued Multiply. Write the product as one power. Add exponents.

9. 4-4 Laws of Exponents Check It Out: Example 1 A. 4 2 4 4 B. x 4 x 2 Multiply. Write the product as one power. = 4 6 4 2 + 4 4 2 4 4 = = x 6 x 4 + 2 x 4 x 2 =

10. 4-4 Laws of Exponents D. p 2 p 2 C. 15 15 2 Check It Out: Example 1 Continued Multiply. Write the product as one power. 15 1 + 2 15 1 15 2 = = 15 3 p 2 + 2 p 2 p 2 = = p 4

11. 4-4 Laws of Exponents Notice what occurs when you divide powers with the same base. 5 5 5353 = 5  5  55  5  5 5  5  5  5  5 = 5  5 = 5 2 = 5  5  55  5  5 5  5  5  5  5

12. 4-4 Laws of Exponents Subtract exponents. 7 2 7 5 – 3 7 5 7 3 Additional Example 2: Dividing Powers with the Same Base Divide. Write the quotient as one power. A. x 10 x 9 B. Subtract exponents. x 10 – 9 x Think: x = x 1

13. 4-4 Laws of Exponents 9 9 9 2 Check It Out: Example 2 Divide. Write the quotient as one power. A. B. n 8 n 5 9 = 9 7 =9 9 – 2 9 9 2 = n 8 – 5 = n 3 n 8 n 5

14. 4-4 Laws of Exponents RAISING A POWER TO A POWER Reading Math (9 ) is read as “nine to the fourth, to the fifth.” 5 4

15. 4-4 Laws of Exponents Simplify. Multiply exponents. Additional Example 3: Raising a Power to a Power A. (5 4 ) 2 (5 4 ) 2 5 4 2 5858 B. (6 7 ) 9 (6 7 ) 9 6 7 9 6 63 Multiply exponents.

16. 4-4 Laws of Exponents Simplify. Multiply exponents. Additional Example 3: Raising a Power to a Power C. D. (17 2 ) –20 (17 2 ) –20 17 2 –20 17 –40 Multiply exponents. 2323 12–3 2323 12 –3

17. 4-4 Laws of Exponents Simplify. Check It Out: Example 3 A. (7 2 ) – 1 B. (7 – 1 ) 2 (7 2 ) – 1 7 2 – 1 7 –2 1 49 = = (7 – 1 ) 2 7 –1 2 7 –2 1 49 = =

18. 4-4 Laws of Exponents Simplify. Check It Out: Example 3 Continued C. D. (5 –2 ) –3 1515 4–2 1515 4 1515 4 = 1515 –8 = =58 = 390,625 (5 –2 ) –3 = 5 –2 –3 = 5 6 = 15,625

19. 4-4 Laws of Exponents Additional Example 4: Application The speed of sound at sea level is 3.4029 x 10 2 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.

20. 4-4 Laws of Exponents Write 5 km as meters. Additional Example 4 Continued distance = rate x time It would take about 1.5 x 10 1 seconds for the sound to reach the shore. 5 km = (3.4029 x 10 2 ) x t 5000 = (3.4029 x 10 2 ) x t 5 x 10 3 = (3.4029 x 10 2 ) x t Write 5000 in scientific notation. 3.4029 x 10 2 5 x 10 3 10 2 = t 1.469 x 10 1  t

21. 4-4 Laws of Exponents 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.) Check It Out: Example 4

22. 4-4 Laws of Exponents Check It Out: Example 4 Continued size of drop 7.6 x 10 –4 mm ≈ 0.2632 x 10 5 = 2.632 x 10 4 size of red blood cell = number of red blood cells in drop; 2 cm = 7.6 x 10 –4 mm 2 mm = 7.6 x 10 –4 2 x 10 1 = 2 7.6 x 10 1 10 –4 cells

23. 4-4 Laws of Exponents Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

24. 4-4 Laws of Exponents Lesson Quiz Write the product or quotient as one power. 3. 8 9 n 7 1. n 3  n 4 10 9 10 5 10 4 4. t 2 5. 3 2 3 3 3 5 3 10 2. 8 8 8 t 9 t 7 6. (m 2 ) 19 m 38 7. (9 -8 ) 9 9 –72 8. (10 4 ) 0 1

25. 4-4 Laws of Exponents 1. Write the product as one power. d 4  d 3 A. d 7 B. d 12 C. 7d D. 12d Lesson Quiz for Student Response Systems

26. 4-4 Laws of Exponents 2. Write the product as one power. 4 4  4 3  4 2 A. 4 9 B. 4 14 C. 4 24 D. 4 432 Lesson Quiz for Student Response Systems

27. 4-4 Laws of Exponents 3. Write the product as one power. (10 –1 ) 0 A. 10 –10 B. 0 C. 1 D. 10 Lesson Quiz for Student Response Systems