1. copyright©amberpasillas2010

2. Exponents give us many shortcuts for multiplying and dividing quickly. Each of the key rules for exponents has an importance in algebra.

3. copyright©amberpasillas2010 2 5 = 2 2 2 2 2 = ? We know 2 2 = 4 4 2 = 8 8 2 = 16 16 2 = 32 So 2 2 2 2 2 = 32

4. copyright©amberpasillas2010 An exponent tells how many times a number is multiplied by itself. 4 3 Base Exponent 444 = 64

5. copyright©amberpasillas2010 How do we write in exponential form ? Answer:

6. copyright©amberpasillas2010 How do we write in exponential form ? Answer: Notice:

7. copyright©amberpasillas2010 Write each in Exponential Form. 2 3 2 3 2 3 2 3  

8. copyright©amberpasillas2010 Write each in Factored Form.

9. copyright©amberpasillas2010 If x 3 means x x x and x 4 means x x x x then what is x 3 x 4 ? x x x x x x x = x 7 Can you think of a quick way to come up with the solution?

10. copyright©amberpasillas2010 Just Add the Exponents ! Your shortcut is called the Product of Powers Property.

11. copyright©amberpasillas2010 When multiplying powers with the same base, just ADD the exponents. For all positive integers m and n: 4 4 4 4 4 3 = 4 2 4 3 + 2 Ex: = = 4 5 4 5

12. copyright©amberpasillas2010 Try This One! What is 31 31 34 34 35?35? Since we are multiplying like bases just add the exponents. Answer: 3(1 3(1 + 4 + 5) 5) = 3 10

13. copyright©amberpasillas2010 Simplify.

14. copyright©amberpasillas2010 Simplify. 1

15. copyright©amberpasillas2010 Simplify.

16. copyright©amberpasillas2010 (7b 5 ) 2 = 7 2 (b 5 ) 2 = 49b 10 (7b 5 )(7b 5 ) Can you think of a quick way to come up with the solution? (5x 3 ) 2 = 5 2 (x 3 ) 2 = 25x 6 (5x 3 )(5x 3 )

17. copyright©amberpasillas2010 Just Multiply the Exponents ! Your short cut is called the Power of a Power Property.

18. copyright©amberpasillas2010 Just Multiply the Exponents ! Your short cut is called the Power of Power Property. (a 2 ) 3 = a 2 a 2 a 2 = a 2+2+2 = a 6

19. copyright©amberpasillas2010 To find the power of a power, you MULTIPLY the exponents. This is used when an exponent is on the outside of parenthesis. 5 3 a 2 3 b 3 (5 1 a 2 b) 3 125a 6 b 3

20. copyright©amberpasillas2010 To find the power of a power, you MULTIPLY the exponents. This is used when an exponent is on the outside of parenthesis. (2 1 x 3 ) 5 2 5 x 3 5 32x 15

21. copyright©amberpasillas2010 6(3 1 y 5 z) 2 6( 3 2 y 5 2 z 2 ) 54 y 10 z 2 6( 9y 5 2 z 2 )

22. copyright©amberpasillas2010 1) 2) Simplify Using What You Just Learned

23. copyright©amberpasillas2010 3)4) Simplify Using What You Just Learned

24. copyright©amberpasillas2010 Simplify Using What You Just Learned 5) 6)

25. copyright©amberpasillas2010 Simplify Using What You Just Learned 7) 8)

26. copyright©amberpasillas2010 Take Out Your Study Guide!!!

27. copyright©amberpasillas2010 Just flip the fraction over to make the exponent positive ! #10

28. copyright©amberpasillas2010 When multiplying powers with the same base, just ADD the exponents. For all positive integers m and n: a m a n = a m + n Ex : #11 (3 2 )(3 3 ) = (3 3) (3 3 3) = 3 2+3 = 3535 (x 5 )(x 4 ) = x 5+4 = x 9

29. copyright©amberpasillas2010 To find the power of a power, you MULTIPLY the exponents. This is used when an exponent is on the outside of parenthesis. # 12 = 5 3 a 2 3 b 3 (5 1 a 2 b) 3 (2 1 x 3 ) 5 = 2 5 x 3 5 8(3 1 y 8 z) 2 = 8 ( 3 2 y 8 2 z 2 ) = 125a 6 b 3 = 32x 15 = 72 y 16 z 2

30. copyright©amberpasillas2010 Extra slides

31. copyright©amberpasillas2010 #11 Simplify.