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Section 4.1 The Product, Quotient, and Power Rules for Exponents
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OBJECTIVES Multiply expressions using the product rule for exponents. A
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OBJECTIVES Divide expressions using the quotient rule for exponents. B
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OBJECTIVES Use the power rules to simplify expressions. C
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RULES Signs for Multiplication 1.When multiplying two numbers with the same sign, product is positive (+).
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RULES Signs for Multiplication 2.When multiplying two numbers with different signs, product is negative (-).
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RULES Signs for Division 1.When dividing two numbers with the same sign, product is positive (+).
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RULES Signs for Division 2.When dividing two numbers with different signs, product is negative (-).
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RULES FOR EXPONENTS If m, n, and k are positive integers, then: 1.Product rule for exponents Example:
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RULES FOR EXPONENTS If m, n, and k are positive integers, then: 2.Quotient rule for exponents
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RULES FOR EXPONENTS If m, n, and k are positive integers, then: 2.Quotient rule for exponents Example:
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RULES FOR EXPONENTS If m, n, and k are positive integers, then: 3.Power rule for products
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RULES FOR EXPONENTS If m, n, and k are positive integers, then: 3.Power rule for products Example:
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RULES FOR EXPONENTS If m, n, and k are positive integers, then: 4.Power rule for quotients
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RULES FOR EXPONENTS If m, n, and k are positive integers, then: 4.Power rule for quotients Example:
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Section 4.1 Exercise #1 Chapter 4 Exponents and Polynomials
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Section 4.1 Exercise #2 Chapter 4 Exponents and Polynomials
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Section 4.2 Integer Exponents
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OBJECTIVES Write an expression with negative exponents as an equivalent one with positive exponents. A
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OBJECTIVES Write a fraction involving exponents as a number with a negative power. B
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OBJECTIVES Multiply and divide expressions involving negative exponents. C
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RULES Zero Exponent If n is a positive integer, Negative Exponent
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RULES n th Power of a Quotient
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RULES For any nonzero numbers x and y and any positive integers m and n: Simplifying Fractions with Negative Exponents
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Section 4.2 Exercise #4 Chapter 4 Exponents and Polynomials
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Simplify and write the answer without negative exponents.
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Section 4.2 Exercise #5 Chapter 4 Exponents and Polynomials
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Section 4.3 Application of Exponents: Scientific Notation
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OBJECTIVES Write numbers in scientific notation. A
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OBJECTIVES Multiply and divide numbers in scientific notation. B Solve applications. C
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RULES A number in scientific notation is written as Where M is a number between 1 and 10 and n is an integer.
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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
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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.
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PROCEDURE Writing a number in scientific notation
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PROCEDURE Multiplying using scientific notation 1.Multiply decimal parts first. Write result in scientific notation.
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PROCEDURE Multiplying using scientific notation 2.Multiply powers of 10 using product rule.
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PROCEDURE Multiplying using scientific notation 3.Answer is product obtained in steps 1 and 2 after simplification.
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Section 4.3 Exercise #6 Chapter 4 Exponents and Polynomials
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Write in scientific notation.
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Section 4.3 Exercise #7 Chapter 4 Exponents and Polynomials
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Perform the indicated operations.
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Section 4.4 Polynomials: An Introduction
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OBJECTIVES Classify polynomials. A Find the degree of a polynomial. B
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OBJECTIVES Write a polynomial in descending order. C Evaluate polynomials. D
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DEFINITION Polynomial An algebraic expression formed using addition and subtraction on products of numbers and variables raised to whole number exponents.
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Section 4.4 Exercise #8 Chapter 4 Exponents and Polynomials
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Classify as a monomial (M), binomial (B), or trinomial (T). B, binomial M, monomial T, trinomial
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Section 4.4 Exercise #10 Chapter 4 Exponents and Polynomials
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Find the value.
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Section 4.5 Addition and Subtraction of Polynomials
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OBJECTIVES Add polynomials. A Subtract polynomials. B
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OBJECTIVES Find areas by adding polynomials. C Solve applications. D
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Section 4.5 Exercise #11 Chapter 4 Exponents and Polynomials
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Add.
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Section 4.5 Exercise #12 Chapter 4 Exponents and Polynomials
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Section 4.6 Multiplication of Polynomials
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OBJECTIVES Multiply two monomials. A Multiply a monomial and a binomial. B
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OBJECTIVES Multiply two binomials using FOIL method. C Solve an application. D
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PROCEDURE First terms multiplied first. FOIL Method for Multiplying Binomials Outer terms multiplied second. Inner terms multiplied third. Last terms multiplied last.
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Section 4.6 Exercise #16 Chapter 4 Exponents and Polynomials
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F O I L
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Section 4.7 Special Product of Polynomials
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OBJECTIVES Expand binomials of the form A B C
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OBJECTIVES Multiply a binomial by a trinomial. D Multiply any two polynomials. E
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SPECIAL PRODUCTS
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PROCEDURE Multiplying Any Two Polynomials (Term-By-Term Multiplication) Multiply each term of one by every term of other and add results.
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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.
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PROCEDURE Appropriate Method for Multiplying Two Polynomials: 2.Are the two binomials in the product the sum and difference of the same two terms?
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PROCEDURE Appropriate Method for Multiplying Two Polynomials: Answer has two terms. If so, use SP4.
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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.
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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.
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Section 4.7 Exercise #18 Chapter 4 Exponents and Polynomials
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Expand.
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Section 4.7 Exercise #19 Chapter 4 Exponents and Polynomials
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Section 4.7 Exercise #20 Chapter 4 Exponents and Polynomials
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Find
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Section 4.8 Division of Polynomials
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OBJECTIVES Divide a polynomial by a monomial. A Divide one polynomial by another polynomial. B
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RULE To Divide A Polynomial By A Monomial Divide each term in polynomial by monomial.
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Section 4.8 Exercise #25 Chapter 4 Exponents and Polynomials
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Divide.
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