1. Lesson 8-1 Multiplying Monomials

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4. Objectives Multiply monomials Simplify expressions involving powers of monomials

5. Vocabulary Monomial – a number, a variable, or a product of a number and one or more variables A single term: 6, 2x, 14xy, -3x 2 y 4 (includes products, but not quotients) Constant – a monomial that is a real number

6. Laws of Exponents Multiplication: (add exponents) b 4  b 6 = b 4+6 = b 10 Division: (subtract exponents) b 6  b 4 = b 6-4 = b 2 Power Raised to a Power: (multiply exponents) (b 2 ) 3 = b 2  3 = b 6 1 2 3 4 1 2 3 4 5 6 1 2 3 4 5 6 7 8 9 10 (b  b  b  b)  (b  b  b  b  b  b) = b  b  b  b  b  b  b  b  b  b b  b  b  b  b  b (b  b  b  b  b  b)  (b  b  b  b) = ---------------------- = b  b b  b  b  b 1 2 1 2 1 2 1 2 3 4 5 6 (b  b)  (b  b)  (b  b) = b  b  b  b  b  b

7. Example 1 xy d. c. b. a. ReasonMonomial?Expression Determine whether each expression is a monomial. Explain your reasoning. The expression is the product of two variables. yes The expression is the product of a number and two variables. yes The expression involves subtraction, not the product, of two variables. no is a real number and an example of a constant.

8. Example 2a Simplify. Commutative and Associative Properties Product of Powers Simplify. Answer:

9. Example 2b Simplify. Communicative and Associative Properties Product of Powers Simplify. Answer:

10. Example 3 Simplify Simplify. Answer: Power of a Power Simplify. Power of a Power

11. Example 4 Geometry: Find the volume of a cube with a side length s = 5xyz Simplify. Answer: VolumeFormula for volume of a cube Power of a Product

12. Example 5 Simplify [(8g 3 h 4 ) 2 ] 2 (2gh 5 ) 4 Power of a Power Power of a Product Power of a Power Commutative Property Answer: Power of Powers

13. Summary & Homework Summary: –A monomial is a number, a variable, or a product of a number and or one or more variables –To multiply two powers that have the same bass, add exponents –To find a power of a power, multiply exponents –The power of a product is the product of powers Homework: –Pg. 413 16-40 even