1. Dealing with Exponents

2. What do exponents mean What does 4 2 ? To multiply 4 by itself 2 times – 4 x 4 Well what about 4 -2 ? or 4 5 x 4 2 ?

3. Dealin with inverses Example: 4 -2 A number or letter raised to a negative power means to flip and simplify Ex. 3 -2 =a -3 = = 5 3 = y 1 3232 1 a3a3 1 5 -3 1 y -1

4. GUIDED PRACTICE for Examples 3 and 4 2.7 –2 = 1 49 3. (–2) –5 = 1 32 –

5. When we have the same numbers or letters being multiplied or divided with different exponents we do something different Multiplication we add the exponents ex. 2 2 2 4 = 2 2+4 = 2 6

6. EXAMPLE 1 Using the Product of Powers Property Simplify x 4 x 7. = x 11 Product of powers property Add exponents. x 4 x 7 = x 4 +7

7. GUIDED PRACTICE for Examples 1 Simplify the expression. Write your answer as a power. 3. a 6 a 9 = a 15 = c 16 4. c c 12 c 3

8. GUIDED PRACTICE for Examples 1 Simplify the expression. Write your answer as a power. = 4 10 = 9 9 2.2. 9 8 9 1.1. 4 6 4 4

9. EXAMPLE 2 Using the Product of Powers Property = 3 3 x 5 = 27x 5 Use properties of multiplication. Product of powers property Add exponents. Evaluate the power. 3 2 x 2 3x 3 Simplify 3 2 x 2 3x 3. = (3 2 3) (x 2 x 3 ) = 3 2+1 x 2+3

10. GUIDED PRACTICE for Examples 2 Simplify the expression. 10 2 s 4 10 4 s 2 5.5. = 1,000,000 s 6

11. GUIDED PRACTICE for Examples 2 Simplify the expression. 6 3 t 5 6 2 t 8 6.6. = 7776 t 13

12. GUIDED PRACTICE for Examples 2 Simplify the expression. 7x 2 7x 4 7.7. = 49 x 6

13. GUIDED PRACTICE for Examples 2 Simplify the expression. = 125 z 10 8.8. 5 2 z 5z 7 z 2

14. Simplify 16. (10v 5 )(-7v 6 u 2 ) 17. (-10e 4 )(2e 5 ) 18. (3i 2 )(-9i 6 n 2 )(-4i 6 n 4 ) 19. (-4m 3 )(-m 2 )(7m 5 v 4 ) 20. (9z 4 )(-8z 2 ) 21. (-8a 4 g 6 )(4a 5 )(-9a 4 ) 22. (-4t 3 g 6 )(-12t 2 g 5 ) 23. (9n 5 )(-n 2 g 6 ) 24. (-10m 6 )(-9m 2 )(12m 2 r 5 ) 25. (11a 5 )(-12a 3 e 5 ) 26. (10h 2 )(-5h 5 ) 27. (-2t 2 y 3 )(9t 3 y 3 )(-6t 3 ) 28. (-4w 6 )(-w 2 s 3 ) 29. (8d 6 )(-6d 2 b 5 ) 30. (10s 4 e 5 )(3s 2 e 5 ) 1. (-11m 4 )(-6m 3 p 2 ) 2. (-2f 3 )(-3f 4 s 3 ) 3. (10v 2 )(v 2 k 6 ) 4. (-5l 6 h 4 )(10l 6 h 6 ) 5. (-5f 2 )(f 3 c 3 ) 6. (-12b 3 z 4 )(-11b 5 z 5 ) 7. (7w 6 m 2 )(9w 3 m 3 ) 8. (-6t 5 )(-5t 6 x 3 ) 9. (4r 5 e 4 )(3r 4 ) 10. (2g 3 )(-3g 6 u 6 ) 11. (-11s 4 )(-5s 3 f 2 )(-2s 6 ) 12. (-5o 3 )(3o 6 )(-7o 2 ) 13. (p 6 )(8p 5 n 4 ) 14. (-6t 4 i 5 )(-10t 4 ) 15. (-8b 2 )(-b 6 q 3 )

15. Dividing Exponents When we have division we subtract the two exponents from themselves. Subtract from the higher number where its at. ex. x 7 x4x4 = x 7-4 =x3x3 j2j2 j 5 = 1 j 5-2 = 1 j3j3

16. Examples 2 3 2 5 = 2 5-3 1 = 1 2 = 1 4 3x 7 9x 4 = 3x 7-4 9 = x3x3 3

17. Simplify 1. (7) 2 ÷ 7 4 2. 9 2 ÷ 9 -3 3. (3) 4 ÷ 3 9 4. 5 8 ÷ 5 5 5. x -3 x 5 6. 2 9 2 -11

18. Homework

19. Scientific Notation Is taking a large number and making it to into a more reasonable number. Ex. 14500000000000 → 1.45 x 10 13 The Only Rule is the Base number has to be between 1 and 10

20. EXAMPLE 1 Writing Numbers in Scientific Notation Stars There are over 300,000,000,000 stars in the Andromeda Galaxy. Write the number of stars in scientific notation. SOLUTION Standard form 300,000,000,000 Scientific notation 3 10 11 Product form 3 100,000,000,000 Move decimal point 11 places to the left.Exponent is 11. ANSWER The number in scientific notation is 3 10 11.

21. GUIDED PRACTICE for Example 1 Write the number in scientific notation. SOLUTION Scientific notation 4 10 3 Product form 4 1000 1. 4000 Standard form 4000

22. GUIDED PRACTICE for Example 1 SOLUTION Standard form 7,300,000 Scientific notation 7.3 10 6 Product form 7.3 1,000,000 2. 7,300,000

23. GUIDED PRACTICE for Example 1 SOLUTION Standard form 63,000,000,000 Scientific notation 6.3 10 10 3. 63,000,000,000 Product form 6.3 10,000,000,000

24. GUIDED PRACTICE for Example 1 SOLUTION Standard form 230,000 Scientific notation 2.3 10 5 Product form 2.3 100,000 4. 230,000

25. GUIDED PRACTICE for Example 1 SOLUTION Standard form 2,420,000 Scientific notation 2.42 10 6 Product form 2.42 1,000,000 5. 2,420,000

26. GUIDED PRACTICE for Example 1 SOLUTION Standard form 105 6. 105 Product form 1.05 100 Scientific notation 1.05 10 2

27. Example 2 Given: 0.000567 Use: 5.67 (moved 4 places) Answer: 5.67 x 10 -4

28. Why did the last slide have the scientific notation to x 10 -4 What definition or rule we make about this

29. Changing scientific notation to standard form.

30. To change scientific notation to standard form… Simply move the decimal point to the right for positive exponent 10. Move the decimal point to the left for negative exponent 10. (Use zeros to fill in places.)

31. Example 3 Given: 5.093 x 10 6 Answer: 5,093,000 (moved 6 places to the right)

32. Example 4 Given: 1.976 x 10 -4 Answer: 0.0001976 (moved 4 places to the left)

33. When multiplying 2 or more scientific numbers we must still follow the rule of Scientific Notation making sure the base is still between 1 and 10 Do the following