1. Exponents

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

3. Definition of Exponent 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. 3 4 = 3 ∙ 3 ∙ 3 ∙ 3

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

6. How to read an Exponent This exponent is read three to the 2 nd power or three squared. It can also be read 3 times itself twice. 3 2 Base Exponent

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

8. What is the Exponent? 2 ∙ 2 ∙ 2 =2 3

9. What is the Exponent? 5 ∙ 5 ∙ 5 ∙ 5 =5 4

10. What is the Base and the Exponent? 7 ∙ 7 ∙ 7 ∙ 7 ∙ 7 =7 5

11. What is the Base and the Exponent? 9 ∙ 9 =9 2

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

13. What is the Base and Exponent in Standard Form? 4 2 = 16

14. What is the Base and Exponent in Standard Form? 2 3 = 8

15. 3 2 = 9

16. 5 3 = 125

17. Exponents use patterns 4³ is 4 ∙ 4 ∙ 4 = 64 4 times itself 3 times 4² is 4 ∙ 4 = 16 or 4 times itself 2 times 4 ¹ is 4 = 4 or 4 times itself just once do you see the pattern? Let’s consider what would 4º How could we get from 16 to 4? What would we get when we do the same to 4

18. Now let’s try negative exponents We will follow the same pattern 4³ = 64 4 ∙4 ∙4 4² = 16 4 ∙4  64 ÷4 4¹ = 4 16÷4 4º = 1 4÷4 What do you think 4 -1 1÷4 4 -1 = 1/4

20. Product law: add the exponents together when multiplying the powers with the same base. Ex: NOTE: This operation can only be done if the base is the same!

21. Quotient law subtract the exponents when dividing the powers with the same base. Ex: NOTE: This operation can only be done if the base is the same!

22. Power of a power: keep the base and multiply the exponents. Ex: NOTE: Multiply the exponents, not add them!

23. Zero exponent law: Any power raised to an exponent of zero equals one. Ex: NOTE: No matter how big the number is, as long as it has zero as an exponent, it equals to one. Except

24. Negative exponents: To make an exponent positive, flip the base. Ex: NOTE: This does not change the sign of the base. This is also a division problem (patterns) Remember 8¹=8 8º= 1 (8÷8) 8 -1 = 1÷8 = 1/8 8 -2 = 1/8 ÷ 8 = 1/64

25. Multiplying Polynomials: In multiplying polynomials, you have to multiply the coefficients and add up the exponents of the variables with the same base. Ex:

26. Please simplify the following equations: Answer: How?:

27. Please simplify the following equations: Answer: How?:

28. Please simplify the following equations: Answer: How?:

29. Please simplify the following equations: Answer: How?:

30. Please simplify the following equations: Answer: How?:

31. Please simplify the following equations: Answer: How?:

32. Review

33. Copy and complete each of the following questions.

34. 1.) 4³ 2.) (2+3)² 3.) 10º 4.) 5 -1 5.) 6 -2 next we will try some written with variables. – Ready for a challenge?

35. 1.) b 2 * b 7 1.) b 9 2.) (p 3 ) 4 2.) p 12 3.) (a 2 ) 3 * a 3 3.) a 9 4.) x 2 * (xy) 2 4.) x 4 y 2 5.) (4m) 2 * m 3 5.) 16m 5 6.) (3a) 3 *(2p) 2 6.) 108a 3 p 2

36. 7.)8 2 *(xy) 2 *2x 7.) 128x 3 y 2 8.) w 3 * (3w) 4 8.) 81w 7 9.) q 0 9.) 1 10.)(a 2 b) 0 10.) 1