College Algebra: building concepts and connections, Enhanced by Revathi Narasimhan;

By Revathi Narasimhan;

In line with years of expertise educating and writing supplemental fabrics for extra conventional precalculus texts, Reva Narasimhan takes a functions-focused method of instructing and studying algebra and trigonometry suggestions. This new sequence builds up appropriate techniques utilizing services as a unifying topic, repeating and increasing on connections to easy features. Visualization and research encourage the functions-based technique, allowing scholars to raised hold the fabric to be used in later calculus classes.

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In Exercises 13 and 14, write the expression as a sum or difference of logarithmic expressions. Eliminate exponents and radicals when possible. 3 13. log ͙ x 2y 4 14. ln(e2x 2y) 25. The depreciation rate of a laptop computer is about 40% per year. If a new laptop computer was purchased for $900, find a function that gives its value t years after purchase. 26. The magnitude of an earthquake is measured on the Richter scale using the formula R(I ) ෇ log ͑II ͒, where I 0 represents the actual intensity of the earthquake and I0 is a baseline intensity used for comparison.

Properties of Rational Exponents Assume that a and b are real numbers and s and t are rational numbers. Whenever s and t indicate even roots, assume that a and b are nonnegative real numbers. Then the following properties hold. 1. as и at ෇ asϩt 4. aϪs ෇ Example 2. (as)t ෇ ast 1 ,a as 0 5. ͩͪ a b s ෇ as ,b bs 3. (ab)s ෇ asbs 0 6. as ෇ asϪt, a at 0 7 Expressions Containing Rational Exponents Evaluate the following expressions without using a calculator. 1)0 (b) ᭤Solution (a) Using the rules for rational exponents, (4)3͞2 ෇ (41͞2)3 ෇ 23 ෇ 8.

3x 2y 2)Ϫ3 In Exercises 9 – 16, simplify each expression without using a calculator. 9. Ϫ32 10. (Ϫ3)2 11. 4Ϫ3 14. (Ϫ3)0 ͩͪ 3 4 ͩ ͪ 28. ͩ ͪ 29. 7x 6y 2 21x 3 30. 6x 3y 4 24x 2y 31. (2y Ϫ3)2 y Ϫ5 32. (Ϫ4x Ϫ1)2 x Ϫ3 33. ͩ ͪ 34. ͩ ͪ 12. 6Ϫ2 13. Ϫ20 15. 27. Ϫ2 16. 2 ■ Integer Exponents and Scientific Notation 19 35. 37. ͩ ͩ ͪ ͪ 4x 3y 2z 3 16x Ϫ2yz Ϫ1 36. 5 Ϫ2 Ϫ2 Ϫ4s t 12s3t 38. ͩ ͩ ͪ ͪ 9x 3y 4z 7 3x Ϫ4y 3z Ϫ1 2 3 5 Ϫ2 Ϫ3 27s z t 3z 2t In Exercises 77 – 82, calculate and round your answer to the correct number of significant figures.

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