1. 8-1 Multiplying Monomials This presentation was created following the Fair Use Guidelines for Educational Multimedia. Certain materials are included under the Fair Use exemption of the U. S. Copyright Law. Further use of these materials and this presentation is restricted.

2. Objectives Students will multiply monomials. Students will simplify expressions involving powers of monomials.

3. Vocabulary Monomial – a number, variable, or a product of numbers and variables. An expression involving a variable in the denominator is NOT a monomial. Constant – a monomial that is a real number Examples of monomials: -5, x, ½a 2

4. Properties Product of Powers – to multiply two powers that have the same base, add the exponents Example 1: (5x 4 )(6x 7 ) (56)(x 4 x 7 ) 30x 11

5. Properties Power of a Power – to find a power of a power, multiply the exponents. Example 2: (k 4 ) 5 k 20 Because (k 4 ) 5 means (k 4 )(k 4 )(k 4 )(k 4 )(k 4 ) and if we add the exponents, we get k 20.

6. Properties Power of a Product – to find the power of a product, find the power of EACH factor and multiply. Example 3: (-2xy) 3 =(-2) 3 (x 3 )(y 3 ) = -8x 3 y 3

7. Simplifying Monomial Expressions To simplify an expression involving monomials, write an equivalent expression in which: Each base appears exactly once There are no powers of powers All fractions are in simplest form.

8. Example 4 (ab 4 )(ab 2 ) =(aa)(b 4b 2 ) =a 2 b 6

9. Example 5 (-7c 3 d 4 )(4cd 3 ) = -74c 3 cd 4d 3 = -28c 4 d 7

10. Example 6 (4cd) 2 (-3d 2 ) 3 =(16c 2 d 2 )(-27d 6 ) =16 -27c 2d 2d 6 = -432c 2 d 8