9-3 Multiplying and Dividing Monomials
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1 Find each product. Express using exponents x 10 x 6 4. w 2 (5w 7 ) 5. Find each quotient. Express using exponents esolutions Manual - Powered by Cognero Page 1
2 7. 8. b 11 b 2 9. CANYONS The Grand Canyon is approximately 2 9 kilometers long. Mariner Valley is a canyon on Mars that is approximately 2 12 kilometers long. About how many times longer is Mariner Valley than the Grand Canyon? Divide the length of Mariner Valley by the length of the Grand Canyon. Mariner Valley is about 2 3 or 8 times longer than the Grand Canyon. Find each product. Express using exponents ( 2) 3 ( 2) a 7 a 2 esolutions Manual - Powered by Cognero Page 2
3 13. (t 3 )(t 3 ) 14. (10x)(4x 7 ) 15. 6p 7 9p m 5 ( 4m 6 ) 17. ( 8s 3 )( 3s 4 ) esolutions Manual - Powered by Cognero Page 3
4 18. Find each quotient. Express using exponents ( 1.5) 8 ( 1.5) esolutions Manual - Powered by Cognero Page 4
5 24. r 20 r ( n) 6 ( n) SOUND Sound intensity is measured in decibels. The decibel scale is based on powers of ten as shown. a. How many times as intense is a rock concert as normal conversation? b. How many times as intense is a vacuum cleaner as a person whispering? a. Divide the intensity of a rock concert by the intensity of a normal conversation. A rock concert is 10 5 or 100,000 times as intense as a normal conversation. b. Divide the intensity of a vacuum cleaner by the intensity of a person whispering. A vacuum cleaner is 10 6 or 1,000,000 times as intense as a person whispering. 27. RUNNING A person weighing 5 3 pounds can experience forces 5 times their body weight while running. Find to find the number of pounds exerted on a person s foot while running. 5 4 or 625 pounds are exerted on a person s foot while running. esolutions Manual - Powered by Cognero Page 5
6 28. SEA CUCUMBERS The largest sea cucumbers are more than 10 2 times longer than the smallest sea cucumbers. If the smallest species of sea cucumbers are about 10 millimeters long, find the approximate length of the largest sea cucumbers. The approximate length of the largest sea cucumbers is 10 3 or 1000 millimeters. 29. HEALTH A nurse draws a sample of blood. A cubic millimeter of the blood contains 22 5 red blood cells and 22 3 white blood cells. Compare the number of red blood cells to the number of white blood cells as a fraction. Explain its meaning. The fraction of the number red blood cells to white blood cells is white blood cell.. For every 484 red blood cells, there is one Find each missing exponent. 30. When multiplying powers, the exponents are added = 3, so (5 1 )(5 2 ) = 5 3. The missing exponent is When multiplying powers, the exponents are added = 15, so (9 10 )(9 5 ) = The missing exponent is When multiplying powers, the exponents are added = 19, so (a 12 )(a 7 ) = a 19. The missing exponent is When dividing powers, the exponents are subtracted = 8, so. The missing exponent is 12. esolutions Manual - Powered by Cognero Page 6
7 34. When dividing powers, the exponents are subtracted. 7 7 = 0, so. The missing exponent is When dividing powers, the exponents are subtracted = 8, so c 10 c 2 = c 8. The missing exponent is 2. esolutions Manual - Powered by Cognero Page 7
8 36. MULTIPLE REPRESENTATIONS In this problem, you will investigate area and volume. The formulas A = s 2 and V = s 3 can be used to find the area of a square and the volume of a cube, respectively, with side length s. a. Tabular Copy and complete the table shown. b. Verbal How are the area and volume each affected if the side length is doubled? tripled? c. Verbal How are the area and volume each affected if the side length is squared? cubed? a. Side Area of Square Volume of Cube (units 3 ) Length (units 2 ) (units) s s 2 s 3 2s 3s (2s) 2 = (2s)(2s) = 4s 2 (3s) 2 = (3s)(3s) = 9s 2 s 2 (s 2 ) 2 = (s 2 )(s 2 ) = s 4 s 3 (s 3 ) 2 = (s 3 )(s 3 ) = s 6 (2s) 3 = (2s)(2s)(2s) = 8s 3 (3s) 3 = (3s)(3s)(3s) = 27s 3 (s 2 ) 3 = (s 2 )(s 2 )(s 2 ) = s 6 (s 3 ) 3 = (s 3 )(s 3 )(s 3 ) = s 9 b. If the side length is doubled, the area is quadrupled and the volume is multiplied by 8. If the side length is tripled, the area is multiplied by 3 2 or 9 and the volume is multiplied by 3 3 or 27. c. If the side length is squared, the area and volume are squared. If the side length is cubed, the area and volume are cubed. Find each product or quotient. Express using exponents. 37. ab 5 8a 2 b 5 esolutions Manual - Powered by Cognero Page 8
9 38. 10x 3 y ( 2xy 2 ) OPEN ENDED Write two algebraic expressions whose quotient is x 5. So, a sample answer is x 7 and x 2. esolutions Manual - Powered by Cognero Page 9
10 42. ERROR ANALYSIS Addison and Noah are multiplying (4a 2 )(4a 3 ). Is either of them correct? Explain your reasoning. Addison is correct. Noah did not multiply the coefficients together. 43. CHALLENGE Use the Quotient of Powers Property and the equation to show that a nonzero number raised to the zero power equals 1. Sample answer: By the Quotient of Powers, or a 0 for a 0. Since, then a 0 = 1. So, any number raised to the zero power must equal REASONING True or false. For any integer a, ( a) 2 = a 2. If true, explain your reasoning. If false, give a counterexample. The statement is false. If a = 3, then ( 3) 2 = 9, but 3 2 = WRITING IN MATH Explain how to use division of powers to divide large numbers. Sample answer: Write the numbers as powers with the same base. Then subtract the exponents. 46. In the metric system, one meter is equal to 10 2 centimeters. One kilometer is 10 3 meters. How many centimeters are in one kilometer? A 1000 B 10,000 C 100,000 D 1,000, = = 10 5 or 100,000 So, the correct answer is choice C. esolutions Manual - Powered by Cognero Page 10
11 47. Which of the following expressions has the same value as 6a 3? F 6 a a a G 6 + a + a + a H 6 + a a a J a a a 6 a a a = 6 a = 6a 3 So, the correct answer is choice F. 48. Which of the following expressions is equivalent to the product of 5a 3 and 3a 8? A 8a 11 B 8a 24 C 15a 11 D 15a 24 So, the correct answer is choice C. 49. SHORT RESPONSE The formula A = bh can be used to find the area of a triangle with base b and height h. Write an expression in simplest form to represent the area of the triangle shown below. Show your work. esolutions Manual - Powered by Cognero Page 11
12 Write the prime factorization of each number. Use exponents for repeated factors ALGEBRA Factor each monomial x a m 3 esolutions Manual - Powered by Cognero Page 12
13 57. 33t MILEAGE Which numbers in the table can be expressed as whole numbers raised to a power? Name the cities and express the numbers as powers. Chicago: 400 = 20 2 ; Evansville: 100 = 10 2 ; Nashville: 125 = 5 3 ; Paducah: 25 = 5 2 ; St. Louis: 225 = REAL ESTATE A commission is a fee paid to a salesperson based on a percent of sales. Suppose a real estate agent earns a 3% commission. What commission would be earned for selling a house for $230,000? To find the commission, use the percent equation to find 3% of $230,000. So, the commission earned is $6900. Find each sum or difference. Write in simplest form. 60. esolutions Manual - Powered by Cognero Page 13
14 Evaluate each expression if a = 3, b = 7, and c = esolutions Manual - Powered by Cognero Page 14
15 esolutions Manual - Powered by Cognero Page 15
4-3 Multiplying and Dividing Monomials
Find each product. Express using positive exponents. 1. 2 4 2 6 5. x 10 x 6 2 10 2. 8 5 8 x 16 6. w 2 (5w 7 ) 8 6 3. 5 6 5 9 5w 9 7. m 8 m 10 5 3 4. 3 2 3 5 8. y 4 y 12 y 8 esolutions Manual - Powered
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