Basic Algebra I, 2nd Edition by Nathan Jacobson

By Nathan Jacobson

"These volumes needs to be considered as a landmark in algebraical literature. the large wealth of fabric, the intensity of remedy, and the masterly exposition render those volumes awfully important. All classes on algebra, from the second one undergraduate 12 months to the expert reports for doctoral scholars, can make the most of this authoritative treatise by means of Professor Jacobson." Walter Ledermann, collage of Sussex Volume1

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715 116. 212 Solve each problem. 117. The highest temperature ever recorded in Juneau, Alaska, was 90°F. The lowest temperature ever recorded there was - 22°F. What is the difference between these two temperatures? ) 118. On August 10, 1936, a temperature of 120°F was recorded in Ponds, Arkansas. On February 13, 1905, Ozark, Arkansas, recorded a temperature of - 29°F. What is the difference between these two temperatures? ) 119. 35 in his checking account. 00, which overdraws his account. 50. 27 from his part-time job at Arby’s.

3 25 6 3 6 3 6 (a) 3 # 3 = 3 squared, or 32 # (b) 6 6 # 6 = 6 cubed, or 63 FIGURE 17 NOW TRY EXERCISE 2 EXAMPLE 2 Evaluate. (a) 72 (b) 1- 722 2 (c) - 7 Evaluate. (a) 52 = 5 # 5 = 25 52 means 5 2 3 2 (b) a b = 3 3 (c) 2 6 = 2 (d) 1- 325 Evaluating Exponential Expressions 5 is used as a factor 2 times. # 5, NOT 5 # 2. # 2 3 # 2 8 = 3 27 #2#2#2#2# 2 3 is used as a factor 3 times. 2 = 64 = 1- 321- 321- 321- 321- 32 = - 243 The base is - 3. (e) 1- 226 = 1- 221- 221- 221- 221- 221- 22 = 64 (f ) The base is - 2.

A is positive for all positive numbers a. Concept Check In Exercises 11 and 12, evaluate each exponential expression. (b) - 82 82 11. (a) (c) 1- 822 (b) - 43 12. (a) 43 (d) - 1- 822 (c) 1- 423 (d) - 1- 423 Write each expression by using exponents. See Example 1. # 13. 10 16. 3 2 19. z # 10 # 10 # 10 14. 8 3 2 #8# 8 15. 17. 1- 921- 921- 92 #z#z#z#z#z# z 20. a 3 4 # 3 4 # 3 4 # 3 4 # 3 4 18. 1- 921- 921- 921- 92 #a#a#a# a Evaluate each expression. See Example 2. 21. 42 22. 2 4 23. 283 24. 913 1 3 25.

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