2. Exponents Exponents - An introduction - By Carol Edelstein David E. Owens Middle School New Milford, NJ

3. Location of an Exponent An exponent is a number high and to the right of a base number. An exponent is a number high and to the right of a base number. 3 4 Base Exponent

4. Definition of Exponent An exponent tells you how many times the base number is multiplied by itself. An exponent tells you how many times the base number is multiplied by itself. 3 4 Base Exponent So, 3 4 is equal to 3 x 3 x 3 x 3. So, 3 4 is equal to 3 x 3 x 3 x 3.

5. How to read an Exponent This exponent is read “three to the fourth power”. This exponent is read “three to the fourth power”. 3 4 This exponent is read “two to the sixth power”. This exponent is read “two to the sixth power”. 2 6

6. How to read an Exponent (the special cases) This exponent is read “seven to the second power” or “seven squared”. This exponent is read “seven to the second power” or “seven squared”. 7 2 This exponent is read “eight to the third power” or “eight cubed”. This exponent is read “eight to the third power” or “eight cubed”. 8 3

7. Practice – Read These Exponents 3 267 235 4

8. Did you get… 3 267 235 4 Two to the third power Seven to the fourth power or Two cubed Three to the second power or Three squared Six to the fifth power

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. 4 2 = 16 4 x 4 = Write the Power in Standard Form Make sure that you do not read this question as 4 x 2.

17. 2 3 = 8 2 x 2 x 2 = 4 x 2 = 8 How did you do?

18. 3 2 = 9 3 x 3 = 9 Write the Power in Standard Form Again, make sure that you do not read this question as 3 x 2.

19. 5 4 = 625 5 x 5 x 5 x5 = 25 x 5 x 5 = 125 x 5 = 625 Write the Power in Standard Form

20. Exponents used in Area Problems Area = length x width Length = 30 ft Width = 15 ft Area = 30 ft x 15ft = 450 ft 2 15ft 30ft Remember: ft 2 = ft x ft

21. Exponents are used in Volume Problems Volume = length x width x height length = 10 cm width = 10 cm height = 20 cm Volume = 20 cm x 10 cm x 10 cm = 2,000 cm 3 10 cm 20 cm Remember: cm 3 = cm x cm x cm

22. Exponents are also used… in scientific notation to express very large or small numbers. in scientific notation to express very large or small numbers. Example: Example: The distance to the sun is about 90,000,000 miles. The distance to the sun is about 90,000,000 miles. Using scientific notation, we can write this number. Using scientific notation, we can write this number. 90,000,000 = 9 x 10 x 10 x 10 x 10 x 10 x 10 x 10 90,000,000 = 9 x 10 x 10 x 10 x 10 x 10 x 10 x 10 9 x 10 7 9 x 10 7 Scientific notation

23. The End The End Congratulations, now you know a little more about exponents.