MULITIPLICATION PROPERTIES OF EXPONENTS September 17, 2012

Basic Terminology BASE EXPONENT means Important Examples

Variable Expressions

MULTIPLICATION PROPERTIES PRODUCT OF POWERS This property is used to combine 2 or more exponential expressions with the SAME base.

I DO: Multiplying Powers with the Same Base A B. k 8 k 10 k 18 k Add exponents. Multiply. Write the product as one power.

D C Think: 7 = 7 1 WE DO : Multiplying Powers with the Same Base Multiply. Write the product as one power. Add exponents.

YOU DO: A B. c 22 c 11 c 33 c Add exponents. Multiply. Write the product as one power.

MULTIPLICATION PROPERTIES POWER TO A POWER This property is used to write an exponential expression as a single power of the base.

RAISING A POWER TO A POWER Reading Math (9 ) is read as “nine to the fourth, to the fifth.” 54

Simplify. Multiply exponents. I DO: Raising a Power to a Power A. (10 -2 ) 2 (10 -2 ) 2 = = B. (6 12 ) 4 (6 12 ) 4 = = 6 48 Multiply exponents.

Simplify. Multiply exponents. WE DO: A. (3 11 ) 4 (3 11 ) 4 = = 3 44 B. (4 15 ) 2 (4 15 ) 2 = = 4 30 Multiply exponents.

Simplify. Multiply exponents. YOU DO: A. (9 12 ) 6 (9 12 ) 6 = = 9 72 B. (11 -4 ) 2 (11 -4 ) 2 = = Multiply exponents.

14 Power of a Product Property To find a power of a product, find the power of EACH factor and multiply. I DO:

15 Practice Power of a Product Property 1. We DO: 2. You Do:

MULTIPLICATION PROPERTIES SUMMARY PRODUCT OF POWERS POWER TO A POWER ADD THE EXPONENTS MULTIPLY THE EXPONENTS

17 Review Multiplication Properties of Exponents Product of Powers Property—To multiply powers that have the same base, ADD the exponents. Power of a Power Property—To find a power of a power, multiply the exponents. Power of a Product Property—To find a power of a product, find the power of each factor and multiply.

Exponent MATHO Place the numbers at in any spot on you MATHO card. Be sure to show all your work for each problem to get participation points. 1 st Winner 2 nd Winner 3rd Winner

1. n 3  n 4

3. (3 3 ) 4

6. (17 2 ) –20

7. x 5 y 2

8. x 2 x 3

9. (6 7 ) 9

10. (13 4 ) –10

13. (5 4 ) 2

14. (9 -8 ) 9

16. n 5 n 7

17. (4 8 ) 2

22. (10 5 ) -6

24. (10 8 ) 6