Warm-up: Add 6 sticks to make 10. No breaking! November 29, 2011 At the end of today, you will be able to Multiply and Divide monomials Warm-up: Add 6 sticks to make 10. No breaking! Final is on Thursday, Dec 15th Final Review Pt. 1 due Friday. Start a few each day. HW 5.1 Pg. 226 #18-40 even Quiz Friday!

Lesson 6.1 Operations with Polynomials A monomial is an expression with one term with numbers, variables, and exponents. 3x2 8xy5z A polynomial is an expression with more than one monomial. -8xy5z + 3x2 + 2y

What is the difference between Product of Powers and Power of a Power? Product of Powers Power of a Power (x3)(x4) (x3)4 (2a3b2)(-3a2b5) (2a3b2)3 = x7 = x12 = -6a5b7 = 8a9b6 ADD exponents when they have the same base. (xa)(xb) = xa+b MULTIPLY exponents (xa)b = xa•b

Practice time! (2a2)(3ab2)(b3) 2. (3x2y3)2 3. (4m)2(2mn)

What is the rule for Quotient of Powers? Quotient of Powers - subtract exponents when they have the same base. Check the rule with the above examples. Does it work?

Practice simplifying monomials 1. 2. 3. 4.

Negative exponents – 2 rules Use the division rule for the following: So what’s the first rule? RULE 1: So

What happens when the negative is in the denominator? So what’s the second rule? RULE 2:

Zero Exponents Why does x0 = 1??? Simplify by canceling: Simplify using division rules: So, what does 70 =? = 1 So, what does 1000 =? So, what does ? = 1 Anything to the zero power equals 1!

Let’s put all of it together. Simplify Let’s put all of it together! Simplify. Assume that no variable equals 0. 1. 2. 3. (xy)0