No calculator necessary. Please do not use a calculator.
Lesson 1.1Unit 1 Homework KeyPerform the following operations leaving your answer as a number to a power. Remember that the parentheses can mean multiply as well.1. 53×57=510 2. (129)120=129 3. t5(t4)t2=t7 4. 41347×410=4165. f5f=f46. u11u4=u7 7. (54)5=5208. (b3)6×(b2)9=b369. (j11)5=j55Evaluate, meaning multiply out the exponents.10. 32×32=81 11. (210)(22)29=812. 53254=25 13. 412410=1614. (53)1×50=12515. (14)2=1Determine if the following equations are true. Justify your answer.16. 122×127=126×123 17. x8x3= x5x 18. (t5)2=(t2)5True; 129=129False; x5≠x4True; t10=t1019. (510)2=(55)5 20. 60×6864= 6460 21. m5×m5=(m10)0False; 520≠525True; 64=64False; m10≠m022. k6k2=k2×k6 23. 74273=73×72 24. 3×3434=(35)1 False; k4≠k8True; 75=75False; 31≠35Determine the appropriate exponent to make the equation true.25. 25×21=23×23 26. p6p2= p7p3 27. (34)3=(36)228. (510)2=(54)5 29. b2×b8b6= b7b3 30. 97×98=(93)531. h10h2=h3×h5 32. 611266=68×68 33. 30×3932=(37)1Lesson 1.2Evaluate the following negative exponents giving your answer as a fraction.1. 5-3=1125 2. 2-2=143. 3-2=194. 7-2=1495. 4-3=1646. 10-3=110007. 10-2=11008. 1-14=1 9. 6-2=13610. 2-4=11611. 9-1=1912. 5-2=12513. 10-4=110,000 14. 8-1=18 15. 3-4=18116. 6-1=1617. 4-2=11618. 11-1=111Simplify the negative exponents giving your answer as a fraction.19. a-3=1a3 20. b-2=1b221. c-5=1c522. d-6=1d623. f-11=1f1124. g-13=1g1325. h-1=1h26. j-4=1j4 27. k-20=1k2028. m-9=1m929. n-7=1n730. p-10=1p10 Lesson 1.3Evaluate the following exponents operations giving your answer as a fraction where necessary.1. 53×5-4=152. (129)(12-7)=144 3. t-5(t4)t2=1t3 4. 434-7×4-10=15. f5f-1=f66. y-4-5=y207. (23)-6×(22)7=1168. 122×12-4=1144 9. k-32k4=1k10 10. 4-24=16411. (5-3)2×59=12512. (0-4)10=?Determine if the following equations are true. Justify your answer.13. 12-2×127=12-8×123 14. x-5x-3= x5x7 15. (t-5)2=(t-2)5False; 125≠1125True; 1x2=1x2True; 1t10=1t1016. (510)2=(5-5)-4 17. 6-6×6864= 6-260 18. m7×m7=(m-7)2True; 520=520True; 162=162False; m14≠1m1419. k-6k2=k2×k-10 20. 7-4273=7×712 21. 3×34310=(35)-1 True; 1k8=1k8False; 1711≠713True; 135=135Determine the appropriate exponent to make the equation true.22. 25×2-8=2-6×23 23. p6p-2= p10p2 24. (3-4)3=(3-2)625. (512)-2=(53)-8 26. b-2×b8b5= b4b3 27. 92×9-8=(9-2)328. h-2h0=h3×h-5 29. 62366=6-8×68 30. 3-43-6×39=(37)-1 Lesson 1.4Round each number to a single digit times a power of ten.1. 1,234,000 2. 190,000 3. 99,000,000 4. 3,499,000≈1×106≈2×105≈1×108≈3×1065. 0.000 000 42 6. 0.000 019 7. 0.000 000 016 87 8. 0.007≈4×10-7≈2×10-5≈2×10-8≈7×10-3Rewrite each number in scientific notation.9. 5,390,000,00010. 10,900,000,000 11. 7,800,000,000 12. 873,000,000=5.39×109=1.09×1010=7.8×109 =8.73×10813. 0.000 000 000 321 14. 0.000 001 987 15. 0.000 000 008 5 16. 0.000 023 9=3.21×10-10=1.987×10-6=8.5×10-9 =2.39×10-517. The Earth has an approximate mass of 5,980,000,000,000,000,000,000,000 kg. =5.98×1024≈6×102418. A quarter (meaning the coin) is 0.000 000 25 of a million dollars. =2.5×10-7≈3×10-719. The mass of a dust particle is 0.000 000 000 753 kg. =7.53×10-10≈8×10-1020. The speed of light is 299,792,458 m/sec. =2.99792458×108≈3×108Rewrite each number in standard form.21. 2.3×101322. 6.07×107 23. 5×101124. 1.8×103=23,000,000,000,000=60,700,000=500,000,000,000=1,80025. 2.3×10-11 26. 6.07×10-927. 5×10-528. 1.8×10-6=0.000 000 000 023=0.000 000 006 07 =0.000 05=0.000 001 8 Choose the most appropriate unit of measurement for the given situation.29. The amount of lava coming from a volcano: fluid ounces per hour, cups per hour, or gallons per hour30. The speed human hair grows: inches per year, feet per year, or yards per year31. The growth of a tree: inches per hour, inches per year, yards per year32. Speed of a swimming dolphin: centimeters per hour, meters per hour, kilometers per hour33. The rate of water flow from a shower head: fluid ounces per minute, cups per minute, gallons per minute34. A cell phone measures 2.3×10-5 kilometers in thickness. Would this be best expressed using kilometers, meters, or centimeters?35. The average pace for a biker is 3.2×106 centimeters per hour. Would this be best expressed using kilometers, meters, or centimeters?36. A bullet travels 3.4×105 millimeters per second. Would this be best expressed using millimeters, centimeters, or meters per second?Lesson 1.5Compute the EXACT answer to each of the following questions giving your answer in scientific notation.1. 3×10-6(3×109)2. 6.8×1092×1053. 4.5×107+41,000,000=9×103=3.4×104=8.6×1074. 8.4×107-3.1×1075. 2.4×104(3,000)6. 5.4×1083,000=5.3×107=7.2×107=1.8×1057. 3.9×1013+4.2×10138. 8.2×10-5-0.000 0599. 1.3×10-4(4.2×1011)=8.1×1013=2.3×10-5=5.46×10710. 4.5×1091.5×101311. 1.3×107+4×10712. 5.2×107-12,000,000=3×10-4=5.3×107=4×107ESTIMATE the answer to each of the following questions giving your answer as single digit times a power of ten. 13. How many times bigger is the distance from Earth to the sun of 9.3×106 miles than the furthest distance from Earth to the moon of 3×105 miles?≈3×101 times farther14. The temperature halfway to the Sun from Mercury is approximately 1,800° C and scientists theorize that it may be up to 26,000 times hotter at the center of the Sun. Approximately how hot is it at the center of the Sun?≈6×107 ℃15. Each shrimp weighs approximately 0.000 27 g and a shrimp company can bring in over 3,100,000,000 shrimp per year. Approximately how much would that many shrimp weigh?≈9×105 g16. The Earth has a mass of about 1×1025 kg. Neptune has a mass of 1.8×1027 kg. How many times bigger is Neptune than Earth?≈2×102 times bigger17. A country has an area of approximately 8,400,000,000 square miles and has approximately 210,000 people. How much area is this per person?≈4×104 sq. miles/person 18. A blue whale can eat 300,000,000 krill in a day. All of that krill weighs approximately 6,300,000,000 mg. About how much does each krill weigh?≈2×101 mg19. The US spends on average 10,200 dollars on each student per year. There are about 77,000,000 students in the United States. How about much money total is spent on students each year?≈8×1011 dollars20. McDonald’s has about 210,000 managers and each makes on average 39,000 dollars per year. How much money does McDonald’s spend on managers each year?≈8×109 dollarsReview Unit 1: Exponents KEYNo calculator necessary. Please do not use a calculator.Unit 1 Goals Know and apply the properties of integer exponents to generate equivalent numerical expressions. (8.EE.1)Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. (8.EE.3)Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology. (8.EE.4)Evaluate, meaning multiply out the exponent, giving your answer as a fraction when necessary.1. 44×4-22. (32)(3-5)3. (62)0 4. 343916127112435. (v6)-36. b8b-2 7. k-10(k-2)8. (5-3)-11v18b101k121259. 2-6×232-5 10. (j3)-2×j611. (m-3)5m512. 464-2×4-6411m2016Determine if the following equations are true. Justify your answer. 13. 8-5×86=80×8 14. (j2)-5=j10j2True, 81=81False, j-10≠j815. m3×m-5m2=m4m0 16. (4-5)4=410-2False, m-4≠m4True, 4-20=4-20Determine the appropriate exponent to make the equation true. 17. p5p-5=(p2)?18. 2-10×22=2-4×2?5-419. f0f-7=f14f?20. 9249-2=9?275Write the following numbers in scientific notation. 21. 9,089,000,000 22. 810,000,000,00023. 0.000 000 27 24. 0.001 069.089×1098.1×10112.7×10-71.06×10-3Write the following numbers in standard form. 25. 5.14×10-6 26. 4.07×10927. 3.1×10-7 28. 7.109×1040.000 005 144,070,000,0000.000 000 3171,090Choose the best unit of measurement for the following problems. 29. Would the weight of a strand of hair, about 6.9×10-5 grams, be best expressed using tons, pounds, or milligrams?Milligrams30. Would the area of the City of Charleston, about 24.9×1011 square centimeters, be best expressed using square kilometers, square meters, or square millimeters?Square kilometersEstimate each of the following as a single digit times a power of ten. Then compute each of the following giving your answer in scientific notation. 31. 2.1×106(500)32. 6.3×1073×10333. 4.2×107-3,000,000≈1×109≈2×104≈4×1071.05×1092.1×1043.9×10734. 6.2×10-6+0.000 00535. 4.8×1034×106 36. 3×10-9(2,300)≈1×10-5≈1×10-3≈6×10-61.12×10-51.2×10-36.9×10-6Answer the following questions giving both an estimated answer (single digit times a power of ten) and a precise answer (scientific notation).37. In the United States, there are approximately 300,000,000 people that use a total of approximately 360,000,000,000 gallons of water in a day. How much water does each person use?≈1×1031.2×10338. A football field has an area of 56,560 ft2 and a tennis court 2,800 ft2. How many times bigger in area is a football field than a tennis court?≈2×1012.02×10139. Three thousand people sued McDonald’s for hot coffee and were compensated at least $280,000 for each person. How much money was distributed in total?≈9×1088.4×10840. There were 9,700,000 Macintosh computers sold in 2008. If Macintosh earns an average of $200 profit per computer sold, how much profit did the company make selling computers in 2008?≈2×1091.94×109 ................
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