Chapter 7 Review Sections labeled at the start of the related problems

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1 Chapter 7 Review Sections labeled at the start of the related problems.6 State whether the equation is an example of the product rule, the quotient rule, the power rule, raising a product to a power, or raising a quotient to a power. ) (x) = x 2) m2 m9 = m Multiply and simplify. Leave your answer in exponential notation. ) x6 x0 4) (-4mz4)(m2z2) Divide and simplify. ) -8x 8y7 4x2y Evaluate. 6) Evaluate -x0 for x = -2. 7) Evaluate (-x)0 for x = -4. Write an equivalent expression without a negative exponent. 8) y - x2 9) x -2y z-7 0) - ) a-2 Write an equivalent expression with negative exponents. 2) 7 ) (-7) 4) 9x Simplify using only positive exponents. Leave the answer in exponenetial notation. ) (x-y-4)(4xy-) 6) 4a -b 9a-7b7 Simplify. Write the answer using only positive exponents. Leave the answer in exponenetial notation. 7) (7) -7 8) (-x4y) 9) -2w7 x 2 Simplify. Write the answer using positive exponents only. Leave the answer in exponenetial notation. 2xy- - 20) x-2y4 2) (rs) 2 (r2s2) 7. Simplify. 6 22) 289 2) Identify the radicand and index. 24) 2ab b2 -

2 For the given function, find the indicated function value, if it exists. If the value does not exist, answer "Does not exist". 2) For g(x) = x2-20, find g(). 26) For g(x) = x2-20, find g(). Simplify. Assume that variables can represent any value. 27) 6y2 28) - x0 Simplify. Unless otherwise specified, assume that variables can represent any number. 29) -2 0) Determine the domain of the function. Express your answer in interval notation. 8) f(x) = x - 7 9) f(x) = 6 x ) f(x) = x Write an equivalent expression using radical notation and, if possible, simplify. Assume that even roots are of nonnegative quantities. 4) x/6 42) m4/ Rewrite using exponential notation. Assume that even roots are of nonnegative quantities and that all denominators are nonzero. 4) 7 7 ) (x - 4) 2) - -2x Simplify. Assume all variables represent nonnegative values. ) z0 4) 9x2 + 6x + 6 ) (x - 9)20 For the given function, find the indicated function value, if it exists. If the value does not exist, answer "Does not exist". 6) For f(x) = x +, find f(-9). 7) For f(x) = 4 x -, find f(-). 44) 7 mn 4) 4 x y Rewrite with positive exponents. Assume that even roots are of nonnegative quantities and that all denominators are nonzero. 46) x-4/ 47) 9p-8/9 Use the laws of exponents to simplify. Do not use negative exponents in the answer. Assume that even roots are of nonnegative quantities and that all denominators are nonzero. 48) x/ x4/ 66/ 49) 6-/ 0) (x/6)/ 2

3 Use rational exponents to simplify. Do not use fraction exponents in the final answer. Assume that even roots are of nonnegative quantities. ) 6 a 2 Find a simplified form of f(x). Assume that x can be any real number. 62) f(x) = 26x0 6) f(x) = 2(x - 4)2 2) ) 6 2x x 4 Simplify. Assume that no radicands were formed by raising negative numbers to even powers. 64) 2x4y 6) 4x4y 4) 7x Solve the problem. ) It was determined that the proper length L of the letters of a word printed on pavement is given by L = d 2.27, where d is the h 7. Multiply. 6) 2 distance of a car from the lettering and h is the height of the eye above the surface of the road. All units are in meters. Find L to the nearest tenth of a meter when h =. m and d = 8 m. Multiply and simplify. Assume all variables represent nonnegative real numbers. Write your answer in radical notation. 66) 27 67) xy xy4 7.4 Simplify by taking the roots of the numerator and the denominator. Assume all variables represent positive numbers. 4 68) 8 69) ) 8p q 8) x 4 y Simplify by factoring. 9) ) 4 26x y8z8 Divide and, if possible, simplify. Assume all variables represent positive real numbers. 7) 4y 7y 60) 70 72) 80x 4y2 6) 26x4y 0x 2y

4 7) 486x 6y 2xy -2 86) ( 9 + 4)( - 6) 87) (2 + 7) 2 74) 60mn Rationalize the denominator. Assume all variables represent positive numbers. 7) 4 88) xy2 xy - xy Rationalize the denominator. Assume all variables represent positive numbers. 2 89) 8-90) ) 0 x 9) x x + y 77) 7 4xy2 Multiply and simplify. Assume all variables represent nonnegative real numbers. Write your answer in radical notation. 7. Add or subtract. Simplify by combining like radical terms, if possible. Assume all variables and radicands represent nonnegative numbers. 78) A) 6 B) 20 7 C) 9 7 D) ) ) x2y xy4 Divide and, if possible, simplify. Assume all variables represent positive real numbers. y 2 9) 4 y 80) 6a - 4 4a a 94) a 4b2 ab 2 8) ) Multiply. Assume that all variables represent nonnegative real numbers. 8) 6 ( + ) 84) ( + 2)( - 2) 8) ( + 4)( 6-7) Solve the problem. Assume all variables represent nonnegative real numbers. 9) For f(x) = 4 x2 and g(x) = 4 6x - 4 x0, find (f g)(x). Solve the problem. 96) For f(x) = x2, find f(7 - ) 7.6 Solve. 97) 8q - 7 = 7 4

5 98) 4x + = 9 99) x + 2 = 00) y = y 0) x = x ) 4 y = 0 0) a - 7 = 2a ) 2x + - x + = 0) x x = 4 06) (x - 6)/2 = -2 Solve the problem. 07) If f(x) = x , find a such that f(a) = A) 2 4 B) C) 29 D) 4 Solve the problem. If necessary, round to the nearest tenth. ) On a sunny day, a tree and its shadow form the sides of a right triangle. If the hypotenuse is m long and the tree is 28 m tall, how long is the shadow? 2) A car dealer advertised a big sale by stretching a string of banners from the top of the building to the edge of the driveway. If the building is 29 m high and the driveway is 44 m from the building, how long is the string of banners? Find the distance between the pair of points. Give your answer in exact form and where appropriate find an approximation to three decimal places. ) (, -) and (7, -7) 4) 9, 22 and 9, 9 22 ) (- 6, 2) and ( 26, - ) Find the midpoint of the segment with the given endpoints. 6) (, -9) and (-, 8) 08) The distance d in miles that can be seen on the surface of the ocean is given by d =.6 h, where h is the height in feet above the surface. How high (to the nearest foot) would a platform have to be to see a distance of 9. miles? 7.7 Find the length of the missing side of the right triangle. Round to three decimal places, if necessary. The legs of the right triangle are represented by a and b, and the hypotenuse is represented by c. 09) a = 2, b = 7 0) b =, c = 22 7) - 2, - 2 and 2, 2 8) ( 7, 7) and ( 0, 6) 7.8 Express in terms of i. 9) -9 20) -89 2) Perform the indicated operation and simplify. Write the answer in the form a + bi. 22) (6-6i) + (4 + i) 2) (4-9i) - ( - 4i) 24) 2i( - 9i)

6 2) ) (4 + 8i)(4-8i) 27) (-9 + 2i)2 28) 2 + i 29) 7 i 0) 8 + 9i 9 - i Find the power of i. ) i4 2) i ) (-i)0 4) i64 + i94 6

7 Answer Key Testname: REVIEW CHAPTER 7 ) The power rule 2) The product rule ) x6 4) -20mz6 ) -2x6y2 6) - 7) 8) x2y 9) y z7 x2 0) ) a2 2) 7- ) (-7)- 9 4) x- ) 20 x2y7 6) a 4 b4 7) 72 8) -27x2y 9) 4w 4 x2 y2 20) 8x 2) r6s2 22) 9 7 2) ) b2 - ; 2) 26) Does not exist 27) 4 y 28) - x 29) -8 0) 4 ) x - 4 7

8 Answer Key Testname: REVIEW CHAPTER 7 2) x ) z 4) x + 6 ) (x - 9)0 6) -2 7) Does not exist 8) [7, ) 9) [-0, ) 40) (-, ) 4) 6 x 42) m4 4) 7/7 44) (mn)/7 4) (xy)/4 46) x4/ 47) p 8/9 9 48) x 49) 69/ 0) x/0 ) a 2) x7 6 2 ) x 4) x ) 0. m 6) 0 7) 270pq xy 8) 4 9) ) 6 6) 6xy( xy2) 62) f(x) = 6x x 6) f(x) = 4 x ) 8xy( xy2) 8

9 Answer Key Testname: REVIEW CHAPTER 7 6) 7xy( xy2) 66) 9 67) x4y6 x2y 68) ) ) 7) 2 4x y4z2 72) 2 x2y 7) xy 74) 2 2mn 00 7) 76) 2x x 77) 42x 8xy 78) C 79) ) - 6a 8) x y2 82) ) ) 7 8) ) ) ) y 6 xy - x4y 89) ) 9) x( x - y) x - 9y 92) xy2 6 x2y 9

10 Answer Key Testname: REVIEW CHAPTER 7 9) 2 y 94) a 7 b4 9) (f g)(x) = x 4 6x - x8 96) ) 7 98) 4 99) 2 00) 0, 9 0) 2 02) No solution 0) 6 04), - 0) -2 06) No solution 07) D 08) 49 ft 09) c = ) a = 4.8 ) 2 m 2) 2.7 m ) ,46 4) ).294 6), - 2 7) - 2, 2 8) 9) i 20) i 2 2) -6i 6 22) 0 - i 2) - i 24) 8 + 0i 2) ) 20 27) 77-6i 7 + 0, ) - i 0

11 Answer Key Testname: REVIEW CHAPTER 7 29) - 7 i 0) i ) 2) -i ) - 4) + i