4/12/10 SWBAT… compute problems involving zero & negative exponents Agenda 1. Write hw in planner 2. Review hw#5 (10 min) 3. Quiz on compound and graphing inequalities (10 min) 4. Get Ready for Chapter 7 (5 min) 5. Lesson on monomials and exponents (25 min)  Zero Exponents  Negative Exponents HW1: Zero and negative exponents

Monomials Ms. Sophia Papaefthimiou Infinity HS

Monday, 4/12Tuesday, 4/13Wednesday, 4/14Thursday, 4/15Friday, 4/16 Get Ready for Ch 7 Exponents Overview Zero Exponents Negative Exponents ½ Day: BZero and negative exponents practice Quiz on zero and negative exponents Multiplying Monomials Product of Powers (1) Power of a Product (2) Power of a Power (3) Monday, 4/19Tuesday, 4/20Wednesday, 4/21Thursday, 4/22Friday, 4/23 Multiplying monomials practice Dividing Monomials Power of a Quotient (4) Quotient of Powers (5) Dividing monomials practice Quiz on mult/div monomials NO CLASSES – Parent-Teacher Conferences Polynomials Standard from Terms Degrees Monday, 4/26Tuesday, 4/27Wednesday, 4/28Thursday, 4/29Friday, 4/30 GAINS testing 9 th and 10 th graders GAINS testing 9 th and 10 th graders NO CLASSES – PSAE testing for 11 th graders Adding and subtracting polynomials

Monday, 4/12Tuesday, 4/13Wednesday, 4/14Thursday, 4/15Friday, 4/16 Get Ready for Ch 7 Exponents Overview Zero Exponents Negative Exponents ½ Day: BZero and negative exponents practice Quiz on zero and negative exponents Multiplying Monomials Product of Powers (1) Power of a Product (2) Power of a Power (3) Monday, 4/19Tuesday, 4/20Wednesday, 4/21Thursday, 4/22Friday, 4/23 Multiplying monomials practice Dividing Monomials Power of a Quotient (4) Quotient of Powers (5) Dividing monomials practice Quiz on mult/div monomials NO CLASSES – Parent-Teacher Conferences Polynomials Standard from Terms Degrees Monday, 4/26Tuesday, 4/27Wednesday, 4/28Thursday, 4/29Friday, 4/30 GAINS testing 9 th and 10 th graders GAINS testing 9 th and 10 th graders NO CLASSES – PSAE testing for 11 th graders Adding and subtracting polynomials Monday, 5/3Tuesday, 5/4Wednesday, 5/5Thursday, 5/6Friday, 5/7 Multiplying polynomials by monomials Multiplying two binomials (FOIL) ½ Day: AAdditional practice: FOIL Investigation: Special products

A monomial is a number, a variable or the product of a number and one or more variables with nonnegative integer exponents. It has only one term. An expression that involves division by a variable, like is not a monomial. Examples of monomials: 3, s, 3s, 3sp

Determine whether each expression is a monomial. Write yes or no. Explain your reasoning. 1.) 10 1.) Yes, this is a constant, so it is a monomial. 2.) f ) No, this expression has addition, so it has more than one term. 3.) h 2 3.) Yes, this expression is a product of variables (h 2 = h ∙ h) 4.) j 4.) Yes, single variables are monomials. 5.) 5.) No, this expression has a variable in the denominator.

Definition of an exponent An exponent tells how many times a number is multiplied by itself. 3 4 = (3)(3)(3)(3) = Base Exponent

How to read an exponent This exponent is read three to the fourth power. 3 4

How to read an exponent (cont’d) This exponent is read three to the 2 nd power or three squared. 3 2

How to read an exponent (cont’d) This exponent is read three to the 3rd power or three cubed. 3 3

Exponents are often used in area problems to show the units are squared Area = (length)(width) Length = 30 ft Width = 15 ft Area = (30 ft)(15 ft) = 450 ft 2 15ft 30ft

Exponents are often used in volume problems to show the units are cubed Volume = (length)(width)(height) Length = 10 cm Width = 10 cm Height = 20 cm Volume = (20cm)(10cm)(10cm) = 2,000 cm

What is the exponent? (5)(5)(5)(5) =5 4

What is the base and the exponent? (7)(7)(7)(7)(7) =7 5

What is the answer? 5 3 = 125

Compute: 0 2 Answer: (0)(0) = 0

Compute: (-4) 2 Answer: (-4)(-4) = 16

Compute: -4 2 Answer: -(4)(4) = -16

Compute: 2 0 Answer: 1 Yes, it’s 1…explanation will follow

Zero Exponent Property Words: Any nonzero number raised to the zero power is equal to 1. Symbols: For any nonzero number a, a 0 = 1. Examples: 1.) 6 0 = 1 3.) -6 0 = -1 5.)6.) 2.) (-6) 0 = 1 4.) (abc) 0 = 1

OYO Problems Simplify each expression: 1. (-4) (Recall PEMDAS - Exponents first!) 3. (5x) 0 5x 0 4. (-4.9) 0 (Recall PEMDAS – Parenthesis first!) 5. [(3x 4 y 7 z 12 ) 5 (–5x 9 y 3 z 4 ) 2 ] 0

WHY is anything to the power zero "1" 3 5 = = = = = = 3 0 = 1

Negative Exponent Property Words: For any nonzero number a and any integer n, a -n is the reciprocal of a n. Also, a n is the reciprocal of a -n. Symbols: Examples:

Examples (cont’d)

OYO Problems