Exponents & Polynomials: Product, Quotient, and Power Rules

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

2. Multiply expressions using the product rule for exponents. A OBJECTIVES

3. Divide expressions using the quotient rule for exponents. B OBJECTIVES

4. Use the power rules to simplify expressions. C OBJECTIVES

5. RULES Signs for Multiplication When multiplying two numbers with the samesign, product is positive (+).

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

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

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

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

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

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

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

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

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

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

16. Chapter 4 Exponents and Polynomials Section 4.1Exercise #1

19. Chapter 4 Exponents and Polynomials Section 4.1Exercise #2

21. Section 4.2 Integer Exponents

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

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

24. Multiply and divide expressions involving negative exponents. C OBJECTIVES

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

26. RULES nth Power of a Quotient

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

28. Chapter 4 Exponents and Polynomials Section 4.2Exercise #4

29. Simplify and write the answer without negative exponents.

30. Simplify and write the answer without negative exponents.

31. Chapter 4 Exponents and Polynomials Section 4.2Exercise #5

34. Section 4.3 Applicationof Exponents:Scientific Notation

35. Write numbers in scientific notation. A OBJECTIVES

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

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

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

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

40. PROCEDURE Writing a number in scientific notation

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

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

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

44. Chapter 4 Exponents and Polynomials Section 4.3Exercise #6

45. Write in scientific notation.

46. Chapter 4 Exponents and Polynomials Section 4.3Exercise #7

47. Perform the indicated operations.

48. Section 4.4 Polynomials:An Introduction

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

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