By Ron Larson

Collage ALGEBRA AND CALCULUS: AN utilized technique, moment variation presents a finished source for faculty algebra and utilized calculus classes. The mathematical strategies and purposes are continually awarded within the related tone and pedagogy to advertise self assurance and a soft transition from one path to the following. The consolidation of content material for 2 classes in one textual content saves teachers time of their course--and saves scholars the price of an additional textbook.

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**Extra info for College Algebra and Calculus: An Applied Approach**

**Example text**

22. 24. 26. 28. 30. 32. ͑Ϫ2w͒ 5x4͑x2͒ 2͑4x 4͒3 ͑6y 2͒͑2y 3͒3 10x 9 4x 6 5 2 2 3 z z 5 5z z7 xn и x2n x3n 2m и 23m 5 и 4Ϫ1 38. 6 и 2Ϫ3 и 3Ϫ1 Ϫ3 40. ͑23 ͒ 42. 4Ϫ1 Ϫ 2Ϫ2 44. Ϫ7xϪ1 10x 4yϪ4 46. 5x2yϪ2 y Ϫ2 48. 5 2z2 Ϫ2 50. y Evaluating Expressions with Exponents In Exercises 51–54, evaluate the expression for the indicated value of x. See Example 3. Expression 4 x 2x2 53. 7xϪ2 51. Value Expression Value x ϭ Ϫ6 52. 4xϪ3 xϭ2 xϭ4 54. 8x0 Ϫ ͑8x͒0 x ϭ Ϫ7 55. Discovery Using your calculator, find the values of 103, 102, 101, 100, 10Ϫ1, and 10Ϫ2.

5z 18. 6z ϩ 5x Ϫ 3y 20. z 2 ϩ 6y Ϫ x 4z Ϫ 2y 22. 20x Identifying the Basic Rules of Algebra In Exercises 23–38, identify the rule(s) of algebra illustrated by the statement. See Example 4. 23. 3 ϩ 4 ϭ 4 ϩ 3 8. Ϫ1, 3 24. x ϩ 9 ϭ 9 ϩ x 25. Ϫ15 ϩ 15 ϭ 0 26. ͑x ϩ 2͒ Ϫ ͑x ϩ 2͒ ϭ 0 27. 2͑x ϩ 3͒ ϭ 2x ϩ 6 28. ͑5 ϩ 9͒͑6͒ ϭ 5͑6͒ ϩ 9͑6͒ 1 29. 2 ͑2 ͒ ϭ 1 1 ͑h ϩ 6͒ ϭ 1, h Ϫ6 30. hϩ6 31. h ϩ 0 ϭ h 32. ͑z Ϫ 2͒ ϩ 0 ϭ z Ϫ 2 33. 57 и 1 ϭ 57 34. 1 и ͑1 ϩ x͒ ϭ 1 ϩ x 35. 6 ϩ ͑7 ϩ 8͒ ϭ ͑6 ϩ 7͒ ϩ 8 36. x ϩ ͑ y ϩ 10͒ ϭ ͑x ϩ y͒ ϩ 10 37.

Similarly, in ͑5x͒3, the parentheses indicate that the exponent applies to the 5 as well as to the x, whereas in 5x3 ϭ 5͑x3͒, the exponent applies only to the x. Example 1 Using Properties of Exponents a. 3Ϫ1 и 34 ϭ 3Ϫ1ϩ4 ϭ 33 ϭ 27 b. 56 ϭ 56Ϫ4 ϭ 52 ϭ 25 54 c. 5 2 5 3 ϭ5и 23 ϭ 5 и 5Ϫ3 и 23 ϭ 5Ϫ2 53 d. ͑Ϫ5 и 23͒2 ϭ ͑Ϫ5͒2 23 8 и 23 ϭ 52 ϭ 25 и ͑23͒2 ϭ 25 и 26 ϭ 25 и 64 ϭ 1600 e. ͑Ϫ3ab 4͒͑4abϪ3͒ ϭ Ϫ3͑4͒͑a͒͑a͒͑b4͒͑bϪ3͒ ϭ Ϫ12a2b f. 3a͑Ϫ4a2͒0 ϭ 3a͑1͒ ϭ 3a, 5xy 3 2 g. ϭ a 0 52͑x3͒2 25x6 ϭ 2 y2 y Checkpoint 1 Evaluate each expression.