1. 3535 18 0 9 3

2. Location of Exponent An An exponent is the small number high and to the right of a regular or base number. 3 4 Base Exponent

3. Definition of Exponent An An exponent tells how many times a number is multiplied by itself. 3 4 Base Exponent

4. What an Exponent Represents An exponent tells how many times a number is multiplied by itself. An exponent tells how many times a number is multiplied by itself. 3 4 = 3 x 3 x 3 x 3

5. How to read an Exponent This This exponent is read three to the fourth power. 3 4 Base Exponent

6. How to read an Exponent This This exponent is read three to the 2 nd 2 nd power or or three squared. 3 2 Base Exponent

7. How to read an Exponent This This exponent is read three to the 3rd power or or three cubed. 3 3 Base Exponent

8. Read These Exponents 32 67 2354

9. What is the Exponent? 2 x 2 x 2 =2 3

10. What is the Exponent? 3 x 3 =3 2

11. What is the Exponent? 5 x 5 x 5 x 5 =5 4

12. What is the Base and the Exponent? 8 x 8 x 8 x 8 =8 4

13. What is the Base and the Exponent? 7 x 7 x 7 x 7 x 7 =7 5

14. What is the Base and the Exponent? 9 x 9 =9 2

15. How to Multiply Out an Exponent to Find the Standard Form = 3 x 3 x 3 x 33 9 27 81 4

16. How to Multiply Out an Exponent to Find the Standard Form = 3 x 3 x 3 x 33 9 4 9 81

17. What is the Standard Form? 4 2 = 16

18. What is the Standard Form? 2 3 = 8

19. 5 3 = 125

20. Exponents Are Often Used in Area Problems to Show the Feet Are Squared Length x width = area 2 15ft. 30ft A pool is a rectangle. Length = 30 ft. Width = 15 ft. Area = 30 x 15 = 450 ft.

21. Exponents Are Often Used in Volume Problems to Show the Centimeters Are Cubed Length x width x height = volume 3 10 20 A box is a rectangle. Length = 10 cm Width = 10 cm Height = 20 cm Volume = 10 x 10 x 20 = 2,000 cm

22. Here Are Some Areas Change Them to Exponents 40 feet squared = 40 ft. 56 sq. inches = 56 in. 38 m. squared = 38 m. 56 sq. cm. = 56 cm. 2 2 2 2

23. Here Are Some Volumes Change Them to Exponents 30 feet cubed = 30 ft. 26 cu. inches = 26 in. 44 m. cubed = 44 m. 56 cu. cm. = 56 cm. 3 3 3 3

24. 2.3 x 10 5

25. 210,000,000,000,000,000,000,000 miles (22 zeros) This number is written in decimal notation. When numbers get this large, it is easier to write them in scientific notation. How wide is our universe?

26. Scientific Notation A number is expressed in scientific notation when it is in the form a x 10 n where a is between 1 and 10 and n is an integer

27. Write the width of the universe in scientific notation. 210,000,000,000,000,000,000,000 miles Where is the decimal point now? After the last zero. Where would you put the decimal to make this number be between 1 and 10? Between the 2 and the 1

28. 2.10,000,000,000,000,000,000,000. How many decimal places did you move the decimal? 23 When the original number is more than 1, the exponent is positive. The answer in scientific notation is 2.1 x 10 23

29. 1) Express 0.0000000902 in scientific notation. Where would the decimal go to make the number be between 1 and 10? 9.02 The decimal was moved how many places? 8 When the original number is less than 1, the exponent is negative. 9.02 x 10 -8

30. Write 28750.9 in scientific notation. 1.2.87509 x 10 -5 2.2.87509 x 10 -4 3.2.87509 x 10 4 4.2.87509 x 10 5

31. 2) Express 1.8 x 10 -4 in decimal notation. 0.00018 3) Express 4.58 x 10 6 in decimal notation. 4,580,000

32. Write in PROPER scientific notation. (Notice the number is not between 1 and 10) 8) 234.6 x 10 9 1. Move the decimal point so that the number is between 1 and 10. 2. To do this the decimal point had to be moved 2 places to the left. 3. This means you would add 2 to the exponent 9 with a result of 11. 2.346 x 10 11

33. Write 531.42 x 10 5 in scientific notation. 1..53142 x 10 2 2.5.3142 x 10 3 3.53.142 x 10 4 4.531.42 x 10 5 5.53.142 x 10 6 6.5.3142 x 10 7 7..53142 x 10 8

34. Write the following in scientific notation. 1. 100,2300,00 2. 48.9 x 10 6 3..000401 4. 701.4 x 10 -8

35. Evaluate each expression if c = -4 and d = 9 c 2 + d 2 (c + d) 3 d 3 – (c 2 – 2)