By Kuttler

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**Extra info for An Introduction To Linear Algebra**

**Example text**

2 INTEGER AND RATIONAL NUMBER EXPONENTS 25 Because radicals are defined in terms of rational powers, the properties of radicals are similar to those of exponential expressions. Properties of Radicals If m and n are natural numbers and a and b are positive real numbers, then Product 1a # 1b = 1ab Quotient 1a n a = n Ab 1b Index 31a = 2a n n n n m n mn A radical is in simplest form if it meets all of the following criteria. 1. The radicand contains only powers less than the index. ) 9 3 2. The index of the radical is as small as possible.

5 - 7( -2) - 16 , 8 = 5 - (- 14) - 2 • Evaluate 23 = 8. = 17 • Perform addition and subtraction from left to right. EXAMPLE 9 • Perform multiplication and division from left to right. Use the Order of Operations Agreement Evaluate: 3 # 5 2 - 6( - 3 2 - 4 2) , ( -15) Solution 3 # 5 2 - 6(-3 2 - 4 2) , ( -15) = 3 # 5 2 - 6( -9 - 16) , ( - 15) = 3 # 5 2 - 6( -25) , ( - 15) • Begin inside the parentheses. = • Evaluate 5 2. 3 # 25 - 6( - 25) , ( -15) = 75 + 150 , (- 15) = 75 + (-10) = 65 Try Exercise 80, page 15 • Simplify - 9 - 16.

27. 6a4 22. (- 6x4y)(7x-3y-5) 24. 8a8 12x3y4 26. 18x5y 2 36a-2b3 28. 4 3ab x 5v4w-3 10v8 -48ab10 -32a b 4 3 31. (x-2y)2(xy)-2 32. (x-1y 2)-3(x2y-4)-3 33. a 35. 3a 2b 3 b 4 2 6a4b ( -4x 2y 3)2 37. a (2xy 2)3 a-2b a3b b -4 2 3 2 3 34. a 36. 4 * 1018) 52. 54. 8 * 10-8) In Exercises 55 to 76, evaluate each exponential expression. 16x4 30. (2a b ) (- 4a b ) 2 2 50. 12x3 29. (-2m n )( -3mn ) 3 2 53. 9 * 10-3 48. 4 * 10-6) 4 2 2ab 2c3 5ab 2 b (- 2ab4)3 x-3y-4 x-2y b 56. - 163>2 57. - 642>3 58. 1254>3 59.

### An Introduction To Linear Algebra by Kuttler

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