Answers (Anticipation Guide And Lesson 7-1)

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Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Chapter 7Before you begin Chapter 7PolynomialsAnticipation GuideDATEPERIODA1StatementA12. The product of (x y) and (x - y) will always equal x 2 - y 2.After you complete Chapter 7D11. The square of r t, (r t) 2, will always equal r 2 t 2.Glencoe Algebra 1Answers3Glencoe Algebra 1 For those statements that you mark with a D, use a piece of paper to write anexample of why you disagree. Did any of your opinions about the statements change from the first column?Chapter 7ADDA7. The sum of the two polynomials (3x 2y - 4xy 2 2y 3) and(6xy 2 2x 2y - 7) in simplest form is 5x 2y 2xy 2 2y 3 - 7.8. (4m 2 2m - 3) - (m 2 - m 3) is equal to 3m 2 m.9. Because there are different exponents in each factor, thedistributive property cannot be used to multiply 3n 3 by(2n 2 4n - 12).10. The FOIL method of multiplying two binomials stands forFirst, Outer, Inner, Last.DD6. The degree of the polynomial 3x 2y 3- 5y 2 8x 3 is 3 because thehighest exponent is 3.523is the same as .A3AADSTEP 2A or D5. A polynomial may contain one or more monomials.24. (5)3. To divide two powers that have the same base, subtractthe exponents.1. When multiplying two powers that have the same base,multiply the exponents.2. (k 3)4 is equivalent to k 12. Reread each statement and complete the last column by entering an A or a D.Step 2STEP 1A, D, or NS Write A or D in the first column OR if you are not sure whether you agree ordisagree, write NS (Not Sure). Decide whether you Agree (A) or Disagree (D) with the statement. Read each statement.Step 17NAMECopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.DATEPERIODand the variables3Chapter 7a3b2c7(5)113. (5a 2bc 3) abc 44a3b4110. (2a 3b)(6b 3)16a37. (2a2)(8a)x74. x(x2)(x4)y61. y(y5)-20x3y5514. (-5xy)(4x2)(y4)20x1011. (-4x3)(-5x7)r2n68. (rs)(rn3)(n2)m65. m ․ m5n92. n2 ․ n7Simplify.Product of PowersSimplify each expression.Exercises (3 ․ 5)(x6 2) 15x8The product is 15x8.․ a n a m n.Glencoe Algebra 1-20x4y6z315. (10x3yz2)(-2xy5z)-6j3k1012. (-3j2k4)(2jk6)4x3y49. (x2y)(4xy3)x76. (-x3)(-x4)-7x63. (-7x2)(x4)Example 2Simplify (-4a3b)(3a2b5).(-4a3b)(3a2b5) (-4)(3)(a3 ․ a2)(b ․ b5) -12(a3 2)(b1 5) -12a5b6The product is -12a5b6.For any number a and all integers m and n, amExample 1Simplify (3x6)(5x2).(3x6)(5x2) (3)(5)(x6 ․ x2)Group the coefficientsProduct of PowersA monomial is a number, a variable, or the product of a number and one ormore variables with nonnegative integer exponents. An expression of the form xn is called apower and represents the product you obtain when x is used as a factor n times. To multiplytwo powers that have the same base, add the exponents.Multiplying MonomialsStudy Guide and InterventionMonomials7-1NAMEAnswers (Anticipation Guide and Lesson 7-1)Lesson 7-1Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Chapter Resources

A2Glencoe Algebra 1Multiplying MonomialsStudy Guide and InterventionDATEFor any number a and all integers m and n, (ab)m ambm.Power of a Product16x2b316a4b328. (4x)2(b3)Chapter 712n12y1016. (-2n6y5)(-6n3y2)(ny)3625a8b5f2113. (25a 2b) 3 abf6-243a15n817. (-3a3n4)(-3a3n)4-48x4y614. (2xy)2(-3x2)(4y4)512x9y32a3b8(5 )11. (-4xy)3(-2x2)31210. (2a3b2)(b3)2-27a b7. (4a2)2(b3)-3a b35. (-3ab4)3n 282. (n )7 41234. -3(ab4)3y 101. (y )5 2Simplify each expression.ExercisesPower of a PowerProduct of Powers2 533Glencoe Algebra 1-768x14y218. -3(2x)4(4x5y)28x17y6z1015. (2x3y2z2)3(x2z)472j10k912. (-3j2k3)2(2j2k)3x10y209. (x2y4)564x b66. (4x2b)3x133. (x ) (x )Group the coefficients and the variablesPower of a ProductPower of a PowerSimplify (-2ab2)3(a2)4.(-2ab2)3(a2)4 (-2ab2)3(a8) (-2)3(a3)(b2)3(a8) (-2)3(a3)(a8)(b2)3 (-2)3(a11)(b2)3 -8a11b6The product is -8a11b6.ExampleWe can combine and use these properties to simplify expressions involving monomials.For any number a and all integers m and n, (am)n amn.Power of a PowerAn expression of the form (xm)n is called a power of a powerand represents the product you obtain when xm is used as a factor n times. To find thepower of a power, multiply exponents.(continued)PERIODCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Chapter 7Simplify Expressions7-1NAMEMultiplying MonomialsSkills PracticeDATEPERIOD81122. (-3y)3 -27y324. (2b3c4)2 4b6c823. (3pr ) 9p rx7Chapter 725.x5x226.c2d27cdcd27.GEOMETRY Express the area of each figure as a monomial.2 220. (p3)12 p362 421. (-6p) 36p29p34p18p418. (-2c4d)(-4cd) 8c5d216. (7a5b2)(a2b3) 7a7b5219. (102)3 106 or 1,000,00033 517. (-5m )(3m ) -15m315. (4xy )(3x y ) 12x y13. (2x2)(3x5) 6x714. (5a7)(4a2) 20a912. (cd2)(c3d2) c4d44 810. (ℓ2k2)(ℓ3k) 5k36411. (a2b4)(a2b2) a b29. (y z)(yz ) y z28. x(x2)(x7) x103 37. a2(a3)(a6) a11Simplify.6. 2a 3b No; this is the sum of two monomials.5. j3k Yes; this is the product of two variables.4. y Yes; single variables are monomials.p2r3. 2 No; this is the quotient, not the product, of two variables.Glencoe Algebra 12. a - b No; this is the difference, not the product, of two variables.1. 11 Yes; 11 is a real number and an example of a constant.Determine whether each expression is a monomial. Write yes or no. Explain.7-1NAMEAnswers (Lesson 7-1)Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Lesson 7-1Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Chapter 7Multiplying MonomialsPracticeDATEPERIOD(36)(3 )4 2 p9)2116 a 2d 68A318a b36a2b463ab216.(25x 2Chapter 7Glencoe Algebra 1Answers8Glencoe Algebra 122. HOBBIES Tawa wants to increase her rock collection by a power of three this year andthen increase it again by a power of two next year. If she has 2 rocks now, how manyrocks will she have after the second year? 26 or 6421. COUNTING A panel of four light switches can be set in 24 ways. A panel of five lightswitches can set in twice this many ways. In how many ways can five light switchesbe set? 25 or 3218.3g12a3b4GEOMETRY Express the volume of each solid as a monomial.15.4a2b14. [(42)2]2 4 or 65,536(4 )112. ad 310. (0.2a2b3)2 0.04a4b6GEOMETRY Express the area of each figure as a monomial.13. (0.4k3)3 0.064k9211. p219. (-18m 2n) 2 - mn 2 -54m5n4(6ab 34 48. (-xy)3(xz) -x4y3z41 37. (-15xy 4) - xy 5x2y73 2 24. (2ab f )(4a b f ) 8a b f46. (4g3h)(-2g5) -8g8h25. (3ad4)(-2a2) -6a3d42 223. (-5x y)(3x ) -15x y6Simplify each expression.21b 3c 22. Yes; this is the product of a number, , and two variables.7b21a 21. No; this involves the quotient, not the product, of variables.Determine whether each expression is a monomial. Write yes or no. Explain yourreasoning.7-1NAMECopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Multiplying Monomials3 ftTTTChapter 7If you then flip the coin two more times,there are 23 22 outcomes that canoccur. How many outcomes can occur ifyou flip the quarter as mentioned aboveplus four more times? Write your answerin the form 2x. 29TTHTHTHHTTHHHTHHTTHHHOutcomes3. PROBABILITY If you flip a coin 3 timesin a row, there are 23 outcomes that canoccur.x2. CIVIL ENGINEERING A developer isplanning a sidewalk for a newdevelopment. The sidewalk can beinstalled in rectangular sections thathave a fixed width of 3 feet and a lengththat can vary. Assuming that eachsection is the same length, express thearea of a 4-section sidewalk as amonomial. 12x9DATEPERIOD44.54.8Women’sHTH268382463Volume (in3)Glencoe Algebra 1The power is one-fourth theprevious amount.b. If the current is reduced by one half,what happens to the power?a. Find the power in a household circuitthat has 20 amperes of current and5 ohms of resistance. 2000 watts5. ELECTRICITY An electrician uses theformula W I2R , where W is the powerin watts, I is the current in amperes, andR is the resistance in ohms.Source: WikiAnswersRadius (in.)BallChild’s4. SPORTS The volume of a sphere is given4 3by the formula V πr , where r is the3radius of the sphere. Find the volume ofair in three different basketballs. Useπ 3.14. Round your answers to thenearest whole number.Word Problem Practice1. GRAVITY An egg that has been fallingfor x seconds has dropped at an averagespeed of 16x feet per second. If the egg isdropped from the top of a building, itstotal distance traveled is the product ofthe average rate times the time. Write asimplified expression to show thedistance the egg has traveled after xseconds. 16x27-1NAMEAnswers (Lesson 7-1)Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Lesson 7-1Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

A4Glencoe Algebra 1EnrichmentPERIOD2. 100002 163. 110000112 1956. 11 10112Chapter 7108. 117 111010124. 101110012 6115114113112111Glencoe Algebra 1m 109lkjihgfedcbaThe American Standard Guide forInformation Interchange (ASCII)7. 29 1110129. The chart at the right shows a set of decimalcode numbers that is used widely in storingletters of the alphabet in a computer’s memory.Find the code numbers for the letters of yourname. Then write the code for your nameusing binary numbers. Answers will vary.5. 8 10002Write each decimal number as a binary number.1. 11112 15Find the decimal value of each binary number.10011012 1 26 0 25 0 24 1 23 1 22 0 21 1 20 1 64 0 32 0 16 1 8 1 4 0 2 1 1 64 0 0 8 4 0 1 77Digital computers store information as numbers. Because the electronic circuits of acomputer can exist in only one of two states, open or closed, the numbers that are stored canconsist of only two digits, 0 or 1. Numbers written using only these two digits are calledbinary numbers. To find the decimal value of a binary number, you use the digits to writea polynomial in 2. For instance, this is how to find the decimal value of the number10011012. (The subscript 2 indicates that this is a binary number.)An Wang (1920–1990) was an Asian-American who became one of the pioneers of thecomputer industry in the United States. He grew up in Shanghai, China, but came to theUnited States to further his studies in science. In 1948, he invented a magnetic pulsecontrolling device that vastly increased the storage capacity of computers. He later foundedhis own company, Wang Laboratories, and became a leader in the development of desktopcalculators and word processing systems. In 1988, Wang was elected to the NationalInventors Hall of Fame.DATECopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Chapter 7An Wang7-1NAME4ab7abSimplify . Assume24-17-2( )( b )Group powers with the same base.Chapter 7(rw )2r 5w 310. 4 3xy 6yx7. y242a4. a a5416r 455 31. 5 or 12523( 2r n ))r 6n 311. 3 5(2a 2b8. ax 5y 3xy45. y5 2mm62. m24253 2 3(2a 3b 5) 3(3b )2 3(a 3) 3(b 5) 3 (3) 3(b 2) 38a 9b 15 27b 68a 9b 9 278a 9b 9.The quotient is 2732a b( 3b )1181 4 8 rn8a3b316m( 3b )Quotient of PowersPower of a PowerPower of a ProductPower of a Quotientnrt32764 6 6 pr17Glencoe Algebra 17 7 2nt12. r r 4n43 3 24p 4 r 43p r( )9. 2 2-2y 714y6. 5 - y 23. p3n32p 5n 4pnSimplify each expression. Assume that no denominator equals zero.Exercisesba m .32a 3b 5Simplify . Assume2mthat no denominator equals zero.Example 2(b)aFor any integer m and any real numbers a and b, b 0, (a )(b ) Quotient of Powers a3b5Simplify.The quotient is a3b5 .aba 4b 7a4 b7 2a 2maam-n.For all integers m and n and any nonzero number a, n athat no denominator equals zero.Example 1Power of a QuotientPERIODTo divide two powers with the same base, subtract theDividing MonomialsQuotient of Powersexponents.DATEStudy Guide and InterventionQuotients of Monomials7-2NAMEAnswers (Lesson 7-1 and Lesson 7-2)Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Lesson 7-2Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Chapter 7DATEDividing MonomialsStudy Guide and Intervention(continued)PERIODA51(a -3-2)(b 6-6)(c 5) ( )Simplify.Negative Exponent and Zero Exponent PropertiesSimplify.Quotient of Powers and Negative Exponent PropertiesGroup powers with the same base.Chapter 7(m t )mt-3 -51t 2 10. m2 3 -17. x6-2xyx4 0bb -44. b-5221. 25 or 32-320w4y(6a b)(b )236abGlencoe Algebra 10121Answers4m 2 n 211. -1( 8m " ) 8. 2 42 6-14w y 25. -1 2-1(-x y)mm2. m5-41p(3rt) ur tu-49ru3m332nGlencoe Algebra 112. - -6 410(-2mn )4m n2 -3 9. -1 2 7112(a 2b 3) 2(ab)6. a6b8-2 3. 311pp-8Simplify each expression. Assume that no denominator equals zero.Exercises616a b c( 16 )( a )( b )( c )41 -5 0 5 a bc41 1 5 (1)c 54 ac5 4a 5c5The solution is .4a 516a b c-34a bSimplify . Assume that no denominator equals zero.2 6 -54a -3b 64 a -3 b 6 1 6 2 6 -52-5ExampleThe simplified form of an expression containing negative exponents must contain onlypositive exponents.a11nFor any nonzero number a and any integer n, a -n n and -n a .Negative Exponent PropertyaFor any nonzero number a, a0 1.Zero ExponentAny nonzero number raised to the zero power is 1; for example,(-0.5)0 1. Any nonzero number raised to a negative power is equal to the reciprocal of the1. These definitions can be used tonumber raised to the opposite power; for example, 6 -3 63simplify expressions that have negative exponents.Negative Exponents7-2NAMECopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Dividing MonomialsSkills PracticeDATEPERIOD1m4a2b3316p 1449r16418-1119 1kChapter 75uu3-15t 0u -125. - 344 2f -5g 4 g hhf 23. -25f -7 1f f 21. 41119. k0(k4)(k-6) 2( 11 )917. 15. 8-2 2 or 424p 77r( )13. 2x7w x3w-21w 5x 211. - 4 53a 3b 59. ab 236n12n 5 n 7. mm 25. 3xwx-2925 12563011348x 6y 7z 5-6xy z8x 5 y 2z26. - 5 615x 6y -95xy16p 5w 22p 3w 3( )24. 3x5y2-1122.k"m20. k-1(ℓ-6)(m3) 6h318. h9-6h(3)516. 1414. 4-4 4 or 32x 3y 2z 5-8xyz12. -4x2yz32m 7p 210. m4m 3p 2w 4x 3 28. x43dt9d6. 3d6rt7r 3t 2 1 4. 3 42x4 23. x212992. 94 or 656186661 or 61. 45Simplify each expression. Assume that no denominator equals zero.7-2NAMEGlencoe Algebra 1Answers (Lesson 7-2)Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Lesson 7-2Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

A6Glencoe Algebra 1Dividing MonomialsPracticeDATEPERIOD85364f 9g 327h1xy 1857p r)2pqr36w 1049p r(3)414. -425681 -5q 10r 25( c dh )7c -3d 326. 5-4-187d hc 2 4j( j -1k 3) -4 23. j 3k 3k 156t 2u 4- x917. 2c4f 7-1 2 -3xy 223 201(2x 3y 2z3 x yz27. 4-2)-29x 24y z 2 6(2a -2b) -3a4 24. 5a 2b 440b 7rr4 21. (3r) 3 2718. -3-3 5( x4 y )11r s22r s15. 2rs52 -3114416x12. 12-2 24x-4x9. - 358y 7z 64y z6. 2yz6 53. xy yChapter 714Glencoe Algebra 129. COUNTING The number of three-letter “words” that can be formed with the Englishalphabet is 263. The number of five-letter “words” that can be formed is 265. How manytimes more five-letter “words” can be formed than three-letter “words”? 67648428. BIOLOGY A lab technician draws a sample of blood. A cubic millimeter of the bloodcontains 223 white blood cells and 225 red blood cells. What is the ratio of white blood1cells to red blood cells? 25. -2q -1r 3qr( )m -2n -5 m 2 22. (m 4n 3) -1 n 25u2 12 6-12t -1u 5x -420. 2t -3ux 5u411. p(q-2)(r-3) 2 3(6w8. 6 3-4c d5d5c 2d 35. - 2abg 8h 26f -2g 3h 5 19. g54f -2g -5h 3949 68c 3d 2f 44c d f-24ab2. a3b333-15w 0u -116. - 34313. (7)10. x3(y-5)(x-8) 5 57. 64f 3g3h( )4. mn4m npmp8884 or 40961. 4Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Chapter 7Simplify each expression. Assume that no denominator equals zero.7-2NAMEDividing Monomials-2Chapter 7103. E-MAIL Spam (also known as junke-mail) consists of identical messagessent to thousands of e-mail users. Peopleoften obtain anti-spam software to filterout the junk e-mail messages theyreceive. Suppose Yvonne’s anti-spamsoftware filtered out 102 e-mails, and shereceived 104 e-mails last year. Whatfraction of her e-mails were filtered out?Write your answer as a monomial.253 15,6252. SPACE The Moon is approximately 254kilometers away from Earth on average.The Olympus Mons volcano on Marsstands 25 kilometers high. How manyOlympus Mons volcanoes, stacked on topof one another, would fit between thesurface of the Earth and the Moon?15DATEPERIODGlencoe Algebra 110c. One kilobyte of memory is what1fraction of one terabyte? 10 -99b. Predict the hard drive capacity in theyear 2025 if this rate of growthcontinues.6.25 petabytesa. The newer hard drives have abouthow many times the capacity of the1995 drives?12,500103 terabytes 1 petabyte103 gigabytes 1 terabyte103 megabytes 1 gigabyte (gig)103 kilobytes 1 megabyte (meg)103 bytes 1 kilobyte8 bits 1 byteMemory Capacity Approximate Conversions5. COMPUTERS In 1995, standard capacityfor a personal computer hard drive was40 megabytes (MB). In 2010, a standardhard drive capacity was 500 gigabytes(GB or Gig). Refer to the table below.105 100,0004. METRIC MEASUREMENT Consider adust mite that measures 10-3 millimetersin length and a caterpillar that measures10 centimeters long. How many times aslong as the mite is the caterpillar?Word Problem Practice1. CHEMISTRY The nucleus of a certainatom is 10-13 centimeters across. If thenucleus of a different atom is 10-11centimeters across, how many times aslarge is it as the first atom? 1007-2NAMEAnswers (Lesson 7-2)Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Lesson 7-2Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Chapter 7EnrichmentDATE10245122561286432168425 152 53 54 55 56 57 58 59 b. 510 4 142 43 44 45 46 47 48 49 c. 410 A750 140 1?0-1 does not exist. 0-2 does not exist. 0-3 does not exist.()Chapter 7Glencoe Algebra 1Answers16Glencoe Algebra 1which is a false result, since division by zero is not allowed. Thus, 00cannot equal 1.01101 0Answers will vary. One answer is that if 0 1, then 1 ,10007. The symbol 00 is called an indeterminate, which means that it has no unique value.Thus it does not exist as a unique real number. Why do you think that 00 cannot equal 1?No, since the pattern 0n 0 breaks down for n 1.6. Based upon the pattern, can you determine whether 00 exists?Negative exponents are not defined unless the base is nonzero.5. Why do 0-1, 0-2, and 0-3 not exist?03 0 02 0 01 0 00 Study the pattern below. Then answer the questions.4. Refer to Exercise 3. Write a rule. Test it on patterns that you obtain using 22, 25, and 24as bases. Any nonzero number to the zero power equals one.20 13. What would you expect the following powers to be?each power, divide the power on the row above by the base (2, 5, or 4).2. Describe the pattern of the powers from the top of the column to the bottom. To getThe exponents decrease by one from each row to the one below.1. Describe the pattern of the exponents from the top of each column to the bottom.Study the patterns for a, b, and c above. Then answer the questions.2 122 23 24 25 26 27 28 29 a. 210 Use your calculator, if necessary, to complete each pattern.Patterns with Powers7-2NAMECopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.DATEScientific NotationStudy Guide and InterventionPERIOD2.002 10-311. 0.0020023.01 10-48. 0.0003011.4 1045. 14,0008.03 10102. 80,300,000,000Chapter 70.000090919. 9.09 10-50.0351720. 3.5 10-210,002,400,00015. 1.00024 101016. 2.001 10-60.0000020010.00003214. 3.2 10-549,10013. 4.91 104Express each number in standard form.1.85 10-710. 0.0000001854.9 10-37. 0.00496.807 10134. 68,070,000,000,0005.1 1061. 5,100,000Glencoe Algebra 117,087,00

Chapter 7 Glencoe Algebra 1 Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 7 Glencoe Algebra 1 a 2 2 3

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the Anticipation Guide as a pretest for the lesson. Hold on to the pretest for debriefing during the assessment section of the lesson plan. Anticipation Guide Puberty Indicate True (T) or False (F) for each statement. _ 1. The changes during puberty are physical rather than emotional. _ 2. Puberty lasts 5 to 7 years in boys. _ 3.