By Ron Larson
Collage ALGEBRA AND CALCULUS: AN utilized procedure, moment version offers a entire source for school algebra and utilized calculus classes. The mathematical strategies and functions are constantly awarded within the comparable tone and pedagogy to advertise self belief and a soft transition from one direction 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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Additional info for College algebra and calculus : an applied approach
5 Ί Ϫ243 ϭ Ϫ3 3 4 813 ϭ 27 10. Ί 12. 32 4 81͒ ϭ 27 9. ͑Ί 11. Rational Exponent Form 1͞5 Ϫ216 ϭ Ϫ6 7. 3 Ί ϭ2 5 64yϪ5 35. Ί 36. 5 4 16xϪ4 y 8 z 4 39. Ί 5 243x 5 yϪ5 z15 40. Ί In Exercises 41– 48, rewrite the expression by rationalizing the denominator. Simplify your answer. 41. 3 Ϫ27 15. ϪΊ 3 0 16. Ί 18. 4 81 Ί 3 4 5624 20. Ί 21. 161͞2 22. 271͞3 23. 363͞2 24. 253͞2 25. Ί2 и Ί3 26. Ί2 27. 28. 30. 43. 45. 47. 3 Ϫ125 19. ͑Ί ͒ 29. 5 96x5 34. Ί 38. Ί3x 2 yz 6 3 64 14. Ί Ϫ3͞4 ͑16 81 ͒ ͑Ϫ 641 ͒Ϫ1͞3 33.
Am͒n ϭ amn 6. aϪn ϭ 8. ab Ϫn ϭ Product of Powers x7 ϭ x7Ϫ4 ϭ x3 x4 Quotient of Powers ͑5x͒3 ϭ 53x3 ϭ 125x3 Power of a Product 2x Power of a Quotient 3 ϭ 23 8 ϭ 3 x3 x ͑ y3͒Ϫ4 ϭ y3͑Ϫ4͒ ϭ yϪ12 1 an 7. a0 ϭ 1, и 34 ϭ 32ϩ4 ϭ 36 1 y4 yϪ4 ϭ a Definition of negative exponent ͑x2 ϩ 1͒0 ϭ 1 0 ba , Power of a Power 32 n a 0, b 0 Խ Խ ԽԽ Ϫ3 ϭ 23 Definition of zero exponent 3 Խ22Խ ϭ Խ2Խ2 ϭ 22 9. a2 ϭ a 2 ϭ a2 Notice that these properties of exponents apply for all integers m and n, not just positive integers.
Add or subtract with like denominators: a c a±c ± ϭ b b b 5. Add or subtract with unlike denominators: 6. Multiply fractions: 7. Divide fractions: a b c 0 a c ad ± bc ± ϭ b d bd ac и d ϭ bd a c a Ϭ ϭ b d b d ad и c ϭ bc , c 0 In Property 1 (equivalent fractions) the phrase “if and only if” implies two statements. One statement is: If a͞b ϭ c͞d, then ad ϭ bc. The other statement is: If ad ϭ bc, where b 0 and d 0, then a͞b ϭ c͞d. 2 Example 5 a. x Ϫ b. ✓CHECKPOINT 5 Simplify the expression x 2x ϩ .