Section 4.1 The Product, Quotient, and Power Rules for Exponents

OBJECTIVES Multiply expressions using the product rule for exponents. A

OBJECTIVES Divide expressions using the quotient rule for exponents. B

OBJECTIVES Use the power rules to simplify expressions. C

RULES Signs for Multiplication 1.When multiplying two numbers with the same sign, product is positive (+).

RULES Signs for Multiplication 2.When multiplying two numbers with different signs, product is negative (-).

RULES Signs for Division 1.When dividing two numbers with the same sign, product is positive (+).

RULES Signs for Division 2.When dividing two numbers with different signs, product is negative (-).

RULES FOR EXPONENTS If m, n, and k are positive integers, then: 1.Product rule for exponents Example:

RULES FOR EXPONENTS If m, n, and k are positive integers, then: 2.Quotient rule for exponents

RULES FOR EXPONENTS If m, n, and k are positive integers, then: 2.Quotient rule for exponents Example:

RULES FOR EXPONENTS If m, n, and k are positive integers, then: 3.Power rule for products

RULES FOR EXPONENTS If m, n, and k are positive integers, then: 3.Power rule for products Example:

RULES FOR EXPONENTS If m, n, and k are positive integers, then: 4.Power rule for quotients

RULES FOR EXPONENTS If m, n, and k are positive integers, then: 4.Power rule for quotients Example:

Section 4.1 Exercise #1 Chapter 4 Exponents and Polynomials

Section 4.1 Exercise #2 Chapter 4 Exponents and Polynomials

Section 4.2 Integer Exponents

OBJECTIVES Write an expression with negative exponents as an equivalent one with positive exponents. A

OBJECTIVES Write a fraction involving exponents as a number with a negative power. B

OBJECTIVES Multiply and divide expressions involving negative exponents. C

RULES Zero Exponent If n is a positive integer, Negative Exponent

RULES n th Power of a Quotient

RULES For any nonzero numbers x and y and any positive integers m and n: Simplifying Fractions with Negative Exponents

Section 4.2 Exercise #4 Chapter 4 Exponents and Polynomials

Simplify and write the answer without negative exponents.

Section 4.2 Exercise #5 Chapter 4 Exponents and Polynomials

Section 4.3 Application of Exponents: Scientific Notation

OBJECTIVES Write numbers in scientific notation. A

OBJECTIVES Multiply and divide numbers in scientific notation. B Solve applications. C

RULES A number in scientific notation is written as Where M is a number between 1 and 10 and n is an integer.

PROCEDURE 1.Move decimal point in number so there is only one nonzero digit to its left. The resulting number is M. Writing a number in scientific notation

PROCEDURE 2.If the decimal point is moved to the left, n is positive; Writing a number in scientific notation If the decimal point is moved to the right, n is negative.

PROCEDURE Writing a number in scientific notation

PROCEDURE Multiplying using scientific notation 1.Multiply decimal parts first. Write result in scientific notation.

PROCEDURE Multiplying using scientific notation 2.Multiply powers of 10 using product rule.

PROCEDURE Multiplying using scientific notation 3.Answer is product obtained in steps 1 and 2 after simplification.

Section 4.3 Exercise #6 Chapter 4 Exponents and Polynomials

Write in scientific notation.

Section 4.3 Exercise #7 Chapter 4 Exponents and Polynomials

Perform the indicated operations.

Section 4.4 Polynomials: An Introduction

OBJECTIVES Classify polynomials. A Find the degree of a polynomial. B

OBJECTIVES Write a polynomial in descending order. C Evaluate polynomials. D

DEFINITION Polynomial An algebraic expression formed using addition and subtraction on products of numbers and variables raised to whole number exponents.

Section 4.4 Exercise #8 Chapter 4 Exponents and Polynomials

Classify as a monomial (M), binomial (B), or trinomial (T). B, binomial M, monomial T, trinomial

Section 4.4 Exercise #10 Chapter 4 Exponents and Polynomials

Find the value.

Section 4.5 Addition and Subtraction of Polynomials

OBJECTIVES Add polynomials. A Subtract polynomials. B

OBJECTIVES Find areas by adding polynomials. C Solve applications. D

Section 4.5 Exercise #11 Chapter 4 Exponents and Polynomials

Add.

Section 4.5 Exercise #12 Chapter 4 Exponents and Polynomials

Section 4.6 Multiplication of Polynomials

OBJECTIVES Multiply two monomials. A Multiply a monomial and a binomial. B

OBJECTIVES Multiply two binomials using FOIL method. C Solve an application. D

PROCEDURE First terms multiplied first. FOIL Method for Multiplying Binomials Outer terms multiplied second. Inner terms multiplied third. Last terms multiplied last.

Section 4.6 Exercise #16 Chapter 4 Exponents and Polynomials

F O I L

Section 4.7 Special Product of Polynomials

OBJECTIVES Expand binomials of the form A B C

OBJECTIVES Multiply a binomial by a trinomial. D Multiply any two polynomials. E

SPECIAL PRODUCTS

PROCEDURE Multiplying Any Two Polynomials (Term-By-Term Multiplication) Multiply each term of one by every term of other and add results.

PROCEDURE Appropriate Method for Multiplying Two Polynomials: 1.Is the product the square of a binomial? Both answers have three terms. If so, use SP2 or SP3.

PROCEDURE Appropriate Method for Multiplying Two Polynomials: 2.Are the two binomials in the product the sum and difference of the same two terms?

PROCEDURE Appropriate Method for Multiplying Two Polynomials: Answer has two terms. If so, use SP4.

PROCEDURE Appropriate Method for Multiplying Two Polynomials: 3.Is the binomial product different from previous two? Answer has three or four terms. If so, use FOIL.

PROCEDURE Appropriate Method for Multiplying Two Polynomials: 4.Is product still different? If so, multiply every term of first polynomial by every term of second and collect like terms.

Section 4.7 Exercise #18 Chapter 4 Exponents and Polynomials

Expand.

Section 4.7 Exercise #19 Chapter 4 Exponents and Polynomials

Section 4.7 Exercise #20 Chapter 4 Exponents and Polynomials

Find

Section 4.8 Division of Polynomials

OBJECTIVES Divide a polynomial by a monomial. A Divide one polynomial by another polynomial. B

RULE To Divide A Polynomial By A Monomial Divide each term in polynomial by monomial.

Section 4.8 Exercise #25 Chapter 4 Exponents and Polynomials

Divide.