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All Textbook Solutions for Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Give an example of a rational number that is not an integer.Given the sets of numbers N (natural numbers), Z (integers), Q (rational numbers), and R (real numbers), indicate to which set (s) each of the following numbers belongs: (a) 8 (b) 2 (c) 1.414 (d) 52Given the sets of numbers N,Z,Q, and R (see Problem 33), indicate to which set(s) each of the following number belongs: (a) 3 (b) 3.14 (c) (d) 23Indicate true (T) or false (F), and for each false statement find real number replacements for a,b, and c that will provide a counterexample. For all real numbers a,b, and c, (A) abc=abc (B) abc=abc (C) abc=abc (D) abc=abcIndicate true (T) or false (F). and for each false statement find real number replacements for a and b that will provide a counterexample. For all real numbers a and b. (A) a+b=b+a (B) ab=ba (C) ab=ba (D) ab=baIf c=0.151515..., then 100c=15.1515... and 100cc=15.1515...0.151515... 99c=15 c=1599=535 Proceeding similarly, convert the repeating decimal 0.090909... into a fraction. (All repeating decimals are rational numbers, and all rational numbers have repeating decimal representations.)Repeat Problem 37 for 0.181818...Use a calculator to express each number in Problems 39 and 40 as a decimal to the capacity of your calculator. Observe the repealing decimal representation of the rational numbers and the nonrepeating decimal representation of the irrational numbers. (a) 136 (b) 21 (c) 716 (d) 29111Use a calculator to express each number in Problems 39 and 40 as a decimal to the capacity of your calculator. Observe the repealing decimal representation of the rational numbers and the nonrepeating decimal representation of the irrational numbers. (a) 89 (b) 311 (c) 5 (d) 11841E42E43E44ESales tax. Find the tax owed on a purchase of $182.39 if the state sales tax rate is 9. (Round to the nearest percentage).Sales tax. If you paid $29.86 in tax on a purchase of $533.19, what was the sales tax rate? (Write as a percentage, rounded to one decimal place).Gasoline prices. If the price per gallon of gas jumped from 4.25 to 4.37, what was the percentage increase? (Round to one decimal place).Gasoline prices. The price of gas increased 4 in one week. If the price last week was 4.30 per gallon, what is the price now? (Round to the nearest cent).(A) Given the polynomial 6x5+7x32, what is the degree of the first term? The second term? The third term? The whole polynomial? (B) Given the polynomial 2u4v25uv3, what is the degree of the first term? The second term? The whole polynomial?Remove parentheses and simplify: (A) 3u22v2+u2+5v2 (B) m33m2+m+12m3m+3 (C) x322x33x+4Add horizontally and vertically: 3x42x34x2,x32x25x.andx2+7x2Subtract 2x25x+4 from 5x28, both horizontally and verticallyMultiply: 2x32x2+3x2 Thus, to multiply two polynomials, multiply each term of one by each term of the other, and combine like terms. Products of binomial factors occur frequently, so it is useful to develop procedures that will enable us to write down their products by inspection. To find the product 2x13x+2 we proceed as follows:Multiply mentally, where possible. (a) 4u3v2u+v (b) 2xy+32xy3 (c) m+4nm4n (d) 2u3v2 (e) 2xy3Perform the indicated operations and simplify: (a) 2t72tt4+t (b) u3v22uv2u+vProblems 1-8 refer to the following polynomials: (A) 2x3 (B) 2x2x+2 (C) x3+2x2x+3 What is the degree of (C)?2E3EProblems 1-8 refer to the following polynomials: (a) 2x3 (b) 2x2x+2 (c) x3+2x2x+3 Add (A) and (B).Problems 1-8 refer to the following polynomials: (a) 2x3 (b) 2x2x+2 (c) x3+2x2x+3 Subtract (B) from (C).Problems 1-8 refer to the following polynomials: (a) 2x3 (b) 2x2x+2 (c) x3+2x2x+3 Subtract (A) from (B).Problems 1-8 refer to the following polynomials: (a) 2x3 (b) 2x2x+2 (c) x3+2x2x+3 Multiply (B) and (C).Problems 1-8 refer to the following polynomials: (a) 2x3 (b) 2x2x+2 (c) x3+2x2x+3 Multiply (A) and (C).In Problems 9-30, perform the indicated operations and simplify. 2u13u+222u3In Problems 9-30, perform the indicated operations and simplify. 2x1+32x34x5In Problems 9-30, perform the indicated operations and simplify. 4a2a53a+2In Problems 9-30, perform the indicated operations and simplify. 2y3y42y1In Problems 9-30, perform the indicated operations and simplify. a+babIn Problems 9-30, perform the indicated operations and simplify. mnm+nIn Problems 9-30, perform the indicated operations and simplify. 3x52x+1In Problems 9-30, perform the indicated operations and simplify. 4t3t2In Problems 9-30, perform the indicated operations and simplify. 2x3yx+2yIn Problems 9-30, perform the indicated operations and simplify. 3x+2yx3yIn Problems 9-30, perform the indicated operations and simplify. 3y+23y2In Problems 9-30, perform the indicated operations and simplify. 2m72m+7In Problems 9-30, perform the indicated operations and simplify. 2x32In Problems 9-30, perform the indicated operations and simplify. 53x2In Problems 9-30, perform the indicated operations and simplify. 4m+3n4m3nIn Problems 9-30, perform the indicated operations and simplify. 3x2y3x+2yIn Problems 9-30, perform the indicated operations and simplify. 3u+4v2In Problems 9-30, perform the indicated operations and simplify. 4xy2In Problems 9-30, perform the indicated operations and simplify. aba2+ab+b2In Problems 9-30, perform the indicated operations and simplify. a+ba2ab+b229E30E31EIn Problems 31-44, perform the indicated operations and simplify. 2x3x+2xx+5+1In Problems 31-44, perform the indicated operations and simplify. x22xy+y2x2+2xy+y2In Problems 31-44, perform the indicated operations and simplify. 3x2y22x+5yIn Problems 31-44, perform the indicated operations and simplify. 5a2b22b+5a2In Problems 31-44, perform the indicated operations and simplify. 2x123x+23x2In Problems 3144, perform the indicated operations and simplify. m22m2m+2In Problems 31-44, perform the indicated operations and simplify. x3x+3x32In Problems 3144, perform the indicated operations and simplify. 32y2x+yx+2y2xyIn Problems 31-44, perform the indicated operations and simplify. 3m+nm3nm+3n3mnIn Problems 31-44, perform the indicated operations and simplify. u+v3In Problems 31-44, perform the indicated operations and simplify. xy3In Problems 31-44, perform the indicated operations and simplify. x2y3In Problems 31-44, perform the indicated operations and simplify. 2mn3Subtract the sum of the last two polynomials from the sum of the first two: 2x2+4xy+y2,3xyy2,x22xyy2,x2+3xy2y2Subtract the sum of the first two polynomials from the sum of the last two: 3m22m+5,4m2m,3m23m2,m3+m2+2In Problems 47-50, perform the indicated operations and simplify. 2x12x3x+12In Problems 47-50, perform the indicated operations and simplify. 5x3x+152x122In Problems 47-50, perform the indicated operations and simplify. 2x3x22x+1x3xx2In Problems 47-50, perform the indicated operations and simplify. 3xxxx2xx+2x23If you are given two polynomials, one of degree m and the other of degree n, where m is greater than n, what is the degree of their product?What is the degree of the sum of the two polynomials in Problem 51 ?How does the answer to Problem 51 change if the two polynomials can have the same degree?How docs the answer to Problem 52 change if the two polynomials can have the same degree?Show by example that, in general, a+b2a2+b2. Discuss possible conditions on a and b that would make this a valid equation.Show by example that, in general, ab2a2b2. Discuss possible conditions on a and b that would make this a valid equation.Investment. You have 10,000 to invest, part at 9 and the rest at 12.If x is the amount invested at 9, write an algebraic expression that represents the total annual income from both investments. Simplify the expression.Investment. A person has 100,000 to invest. If x are invested in a money market account yielding 7 and twice that amount in certificates of deposit yielding 9, and if the rest is invested in high-grade bonds yielding 11, write an algebraic expression that represents the total annual income from all three investments. Simplify the expression.Gross receipts. Four thousand tickets are to be sold for a musical show. If x tickets are to be sold for 20 each and three times that number for 30 each, and if the rest are sold for 50 each, write an algebraic expression that represents the gross receipts from ticket sales, assuming all tickets are sold. Simplify the expression.Gross receipts. Six thousand tickets are to be sold for a concert, some for 20 each and the rest for 35 each. If x is the number of 20 tickets sold, write an algebraic expression that represents the gross receipts from ticket sales, assuming all tickets are sold. Simplify the expression.Nutrition. Food mix A contains 2 fat, and food mix B contains 6 fat. A 10 -kilogram diet mix of foods A and B is formed. If x kilograms of food A are used, write an algebraic expression that represents the total number of kilograms of fat in the final food mix. Simplify the expression.Nutrition. Each ounce of food M contains 8 units of calcium, and each ounce of food N contains 5 units of calcium. A 160-ounce diet mix is formed using foods M and N. If x is the number of ounces of food M used, write an algebraic expression that represents the total number of units of calcium in the diet mix. Simplify the expression.Factor out all factors common to all terms. (a) 2x3y8x2y26xy3 (b) 2x3x273x2Factor by grouping. (A) 6x2+2x+9x+3 (B) 2u2+6uv3uv9v2 (C) ac+bd+bc+adFactor, if possible, using integer coefficients. (A) 2x2+11x6 (B) 4x2+11x6 (C) 6x2+5xy4y2Factor completely: (A) x2+6xy+9y2 (B) 9x24y2 (C) 8m31 (D) x3+y3z3 (E) 9m324n2Factor completely. (A) 18x38x (B) 4m3n2m2n2+2mn3 (C) 2t416t (D) 2y45y2121E2E3EIn Problems 1-8, factor out all factors common to all terms. 10x3y+20x2y215xy3In Problems 1-8, factor out all factors common to all terms. 7m2m3+52m3In Problems 1-8, factor out all factors common to all terms. 5xx+13x+1In Problems 1-8, factor out all factors common to all terms. 4ab2c+d2c+dIn Problems 1-8, factor out all factors common to all terms. 12ab2c15bb2cIn Problems 9-18, factor by grouping. 2x2x+4x2In Problems 9-18, factor by grouping. x23x+2x6In Problems 9-18, factor by grouping. 3y23y+2y2In Problems 9-18, factor by grouping. 2x2x+6x3In Problems 9-18, factor by grouping. 2x2+8xx4In Problems 9-18, factor by grouping. 6x2+9x2x3In Problems 9-18, factor by grouping. wywz+xyxzIn Problems 9-18, factor by grouping. ac+ad+bc+bd17EIn Problems 9-18, factor by grouping. ab+6+2a+3bIn Problems 19-56, factor completely. If a polynomial cannot be factored, say so. 3y2y2In Problems 19-56, factor completely. If a polynomial cannot be factored, say so. 2y2+5x3In Problems 19-56, factor completely. If a polynomial cannot be factored, say so. u22uv15v2In Problems 19-56, factor completely. If a polynomial cannot be factored, say so. x24xy12y2In Problems 19-56, factor completely. If a polynomial cannot be factored, say so. m26m3In Problems 19-56, factor completely. If a polynomial cannot be factored, say so. x2+x4In Problems 19-56, factor completely. If a polynomial cannot be factored, say so. w2x2y2In Problems 19-56, factor completely. If a polynomial cannot be factored, say so. 25m216n227EIn Problems 19-56, factor completely. If a polynomial cannot be factored, say so. x2+10xy+25y2In Problems 19-56, factor completely. If a polynomial cannot be factored, say so. y2+16In Problems 19-56, factor completely. If a polynomial cannot be factored, say so. u2+81In Problems 19-56, factor completely. If a polynomial cannot be factored, say so. 4z228z+48In Problems 19-56, factor completely. If a polynomial cannot be factored, say so. 6x2+48x+72In Problems 19-56, factor completely. If a polynomial cannot be factored, say so. 2x424x3+40x2In Problems 19-56, factor completely. If a polynomial cannot be factored, say so. 2y322y2+48yIn Problems 19-56, factor completely. If a polynomial cannot be factored, say so. 4xy212xy+9xIn Problems 19-56, factor completely. If a polynomial cannot be factored, say so. 16x2y8xy+yIn Problems 19-56, factor completely. If a polynomial cannot be factored, say so. 6m2mn12n2In Problems 19-56, factor completely. If a polynomial cannot be factored, say so. 6s2+7st3t2In Problems 19-56, factor completely. If a polynomial cannot be factored, say so. 4u3vuv3In Problems 19-56, factor completely. If a polynomial cannot be factored, say so. x3y9xy3In Problems 19-56, factor completely. If a polynomial cannot be factored, say so. 2x32x2+8xIn Problems 19-56, factor completely. If a polynomial cannot be factored, say so. 3m36m2+15mIn Problems 19-56, factor completely. If a polynomial cannot be factored, say so. 8x327y3In Problems 19-56, factor completely. If a polynomial cannot be factored, say so. 5x3+40y3In Problems 19-56, factor completely. If a polynomial cannot be factored, say so. x4y+8xyIn Problems 19-56, factor completely. If a polynomial cannot be factored, say so. 8a31In Problems 19-56, factor completely. If a polynomial cannot be factored, say so. x+229y2In Problems 19-56, factor completely. If a polynomial cannot be factored, say so. ab24cd2In Problems 19-56, factor completely. If a polynomial cannot be factored, say so. 5u2+4uv2v2In Problems 19-56, factor completely. If a polynomial cannot be factored, say so. 3x22xy4y2In Problems 19-56, factor completely. If a polynomial cannot be factored, say so. 6xy2+23xy4In Problems 19-56, factor completely. If a polynomial cannot be factored, say so. 4A+B25A+B6In Problems 19-56, factor completely. If a polynomial cannot be factored, say so. y43y24In Problems 19-56, factor completely. If a polynomial cannot be factored, say so. m4n4In Problems 19-56, factor completely. If a polynomial cannot be factored, say so. 15yxy3+12xxy2In Problems 19-56, factor completely. If a polynomial cannot be factored, say so. 15x23x14+60x33x13In Problems 57-60, discuss the validity of each statement. If the statement is true, explain why. If not, give a counterexample. If n is a positive integer greater than 1, then unnn can be factored.In Problems 57-60, discuss the validity of each statement. If the statement is true, explain why. If not, give a counterexample. If m and n are positive integers and mn, then umvn is not factorable.In Problems 57-60, discuss the validity of each statement. If the statement is true, explain why. If not, give a counterexample. If n is a positive integer greater than 1, then un+nn can be factored.In Problems 57-60, discuss the validity of each statement. If the statement is true, explain why. If not, give a counterexample. If k is a positive integer, then 22k+1+v2k+1 can be factored.Reduce each fraction to lowest terms. (a) 1234512123 (b) 149161234Reduce each rational expression to lowest terms. (a) x26x+9x29 (b) x31x21Perform the indicated operations and reduce to lowest terms. (a) 12x2y32xy2+6xyy2+6y+93y3+9y2 (b) 4xx2165Combine into a single fraction and reduce to lowest terms. (A) 528110+635 (B) 14x22x+13x3+312x (C) 2x24x+4+1x1x2Express as a simple fraction reduced to lowest terms: (a) 12+h12h (b) abbaab+2+baIn Problems 1-22, perform the indicated operations and reduce answers to lowest terms. 5913357In Problems 1-22, perform the indicated operations and reduce answers to lowest terms. 1098321In Problems 1-22, perform the indicated operations and reduce answers to lowest terms. 12111094321In Problems 1-22, perform the indicated operations and reduce answers to lowest terms. 15105201510In Problems 1-22, perform the indicated operations and reduce answers to lowest terms. d53ad26a2a4d3In Problems 1-22, perform the indicated operations and reduce answers to lowest terms. d53zd26d4a4d3In Problems 1-22, perform the indicated operations and reduce answers to lowest terms. x212+x18130In Problems 1-22, perform the indicated operations and reduce answers to lowest terms. 2y18128y42In Problems 1-22, perform the indicated operations and reduce answers to lowest terms. 4m318m3+34m2m16m2In Problems 1-22, perform the indicated operations and reduce answers to lowest terms. 3x+84x22x1x358xIn Problems 1-22, perform the indicated operations and reduce answers to lowest terms. x29x23xx2x12In Problems 1-22, perform the indicated operations and reduce answers to lowest terms. 2x2+7x+34x21x+3In Problems 1-22, perform the indicated operations and reduce answers to lowest terms. 2x1x3In Problems 1-22, perform the indicated operations and reduce answers to lowest terms. 5m232m+1In Problems 1-22, perform the indicated operations and reduce answers to lowest terms. 2x+125x2x2In Problems 1-22, perform the indicated operations and reduce answers to lowest terms. 2x+125x2x2In Problems 1-22, perform the indicated operations and reduce answers to lowest terms. x+1x11In Problems 1-22, perform the indicated operations and reduce answers to lowest terms. m3m1m2In Problems 1-22, perform the indicated operations and reduce answers to lowest terms. 3a121aIn Problems 1-22, perform the indicated operations and reduce answers to lowest terms. 5x323xIn Problems 1-22, perform the indicated operations and reduce answers to lowest terms. 2xx216x4x2+4xIn Problems 1-22, perform the indicated operations and reduce answers to lowest terms. m+2m22mmm24In Problems 23-34, perform the indicated operations and reduce answers to lowest terms. Represent any compound fractions as simple fractions reduced to lowest terms. x2x2+2x+1+x13x+316In Problems 23-34, perform the indicated operations and reduce answers to lowest terms. Represent any compound fractions as simple fractions reduced to lowest terms. yy2y21y2+5y142y2+8y+7In Problems 23-34, perform the indicated operations and reduce answers to lowest terms. Represent any compound fractions as simple fractions reduced to lowest terms. 1xy2yxIn Problems 23-34, perform the indicated operations and reduce answers to lowest terms. Represent any compound fractions as simple fractions reduced to lowest terms. 2534x+1In Problems 23-34, perform the indicated operations and reduce answers to lowest terms. Represent any compound fractions as simple fractions reduced to lowest terms. c+25c5c23c3+c1cIn Problems 23-34, perform the indicated operations and reduce answers to lowest terms. Represent any compound fractions as simple fractions reduced to lowest terms. x+7axbx+y+9byayIn Problems 23-34, perform the indicated operations and reduce answers to lowest terms. Represent any compound fractions as simple fractions reduced to lowest terms. 1+3xx9xIn Problems 23-34, perform the indicated operations and reduce answers to lowest terms. Represent any compound fractions as simple fractions reduced to lowest terms. 1y2x21yxIn Problems 23-34, perform the indicated operations and reduce answers to lowest terms. Represent any compound fractions as simple fractions reduced to lowest terms. 12x+h12xhIn Problems 23-34, perform the indicated operations and reduce answers to lowest terms. Represent any compound fractions as simple fractions reduced to lowest terms. 1x+h1xhIn Problems 23-34, perform the indicated operations and reduce answers to lowest terms. Represent any compound fractions as simple fractions reduced to lowest terms. xy2+yxxyyxIn Problems 23-34, perform the indicated operations and reduce answers to lowest terms. Represent any compound fractions as simple fractions reduced to lowest terms. 1+2x15x21+4x5x2In Problems 35-42, imagine that the indicated “ solutions” were given to you by a student whom you were tutoring in this class. (A) Is the solution correct?. If the solution is incorrect, explain what is wrong and how it can be corrected. (B) Show a correct solution for each incorrect solution. x2+4x+3x+3=x2+4xx=x+4In Problems 35-42, imagine that the indicated “ solutions” were given to you by a student whom you were tutoring in this class. (A) Is the solution correct?. If the solution is incorrect, explain what is wrong and how it can be corrected. (B) Show a correct solution for each incorrect solution. x23x4x4=x23xx=x3In Problems 35-42, imagine that the indicated “ solutions” were given to you by a student whom you were tutoring in this class. (A) Is the solution correct?. If the solution is incorrect, explain what is wrong and how it can be corrected. (B) Show a correct solution for each incorrect solution. x+h2x2h=x+12x2=2x+1In Problems 35-42, imagine that the indicated “ solutions” were given to you by a student whom you were tutoring in this class. (A) Is the solution correct?. If the solution is incorrect, explain what is wrong and how it can be corrected. (B) Show a correct solution for each incorrect solution. x+h3x3h=x+13x2=3x2+3x+1In Problems 35-42, imagine that the indicated “ solutions” were given to you by a student whom you were tutoring in this class. (A) Is the solution correct?. If the solution is incorrect, explain what is wrong and how it can be corrected. (B) Show a correct solution for each incorrect solution. x23xx22x3+x3=x23x+x3x22x3=1In Problems 35-42, imagine that the indicated “ solutions” were given to you by a student whom you were tutoring in this class. (A) Is the solution correct?. If the solution is incorrect, explain what is wrong and how it can be corrected. (B) Show a correct solution for each incorrect solution. 2x1x+3x21=2x+2x3x21=1x+1In Problems 35-42, imagine that the indicated “solutions” were given to you by a student whom you were tutoring in this class. (A) Is the solution correct?. If the solution is incorrect, explain what is wrong and how it can be corrected. (B) Show a correct solution for each incorrect solution. 2x2x24xx2=2x2x22xx24=xx+2In Problems 35-42, imagine that the indicated “solutions” were given to you by a student whom you were tutoring in this class. (A) Is the solution correct?. If the solution is incorrect, explain what is wrong and how it can be corrected. (B) Show a correct solution for each incorrect solution. x+x2x23x+2=x+x2x23x+2=2x2Represent the compound fractions in Problems 43-46 as simple fractions reduced to lowest terms. 13x+h213x2hRepresent the compound fractions in Problems 43-46 as simple fractions reduced to lowest terms. 1x+h21x2hRepresent the compound fractions in Problems 43-46 as simple fractions reduced to lowest terms. x211xRepresent the compound fractions in Problems 43-46 as simple fractions reduced to lowest terms. 2112a+2Simplify.and express the answers using positive exponents only. (A) 3y42y3 (B) m2m6 (C) u3v22 (D) y6y21 (E) 8x2y46x5y2Write 1+x11x2 as a simple fraction with positive exponents.(A) Write each number in scientific notation: 47,100;2,443,000,000;1.45 (B) Write each number in standard decimal form: 3.07108;5.98106In Problems 1-14, simplify and express answers using positive exponents only. Variables are restricted to avoid division by 0. 2x9In Problems 1-14, simplify and express answers using positive exponents only. Variables are restricted to avoid division by 0. 3y5In Problems 1-14, simplify and express answers using positive exponents only. Variables are restricted to avoid division by 0. 32w7In Problems 1-14, simplify and express answers using positive exponents only.Variables are restricted to avoid division by 0. 54x9In Problems 1-14, simplify and express answers using positive exponents only.Variables are restricted to avoid division by 0. 2x8x5In Problems 1-14, simplify and express answers using positive exponents only. Variables are restricted to avoid division by 0. 3c9c4In Problems 1-14, simplify and express answers using positive exponents only.Variables are restricted to avoid division by 0. w8w3In Problems 1-14, simplify and express answers using positive exponents only.Variables are restricted to avoid division by 0. m11m5In Problems 1-14, simplify and express answers using positive exponents only.Variables are restricted to avoid division by 0. 2a3210E11E12E13E14E15E16EIn Problems 15-20, write each number in scientific notation. 0.783In Problems 15-20, write each number in scientific notation. 0.019In Problems 15-20, write each number in scientific notation. 0.000034In Problems 15-20, write each number in scientific notation. 0.000000007832In Problems 21-28, write each number in standard decimal notation. 4104In Problems 21-28, write each number in standard decimal notation. 9106In Problems 21-28, write each number in standard decimal notation. 7103In Problems 21-28, write each number in standard decimal notation. 2105In Problems 21-28, write each number in standard decimal notation. 6.171107In Problems 21-28, write each number in standard decimal notation. 3.044103In Problems 21-28, write each number in standard decimal notation. 8.08104In Problems 21-28, write each number in standard decimal notation. 1.13102In Problems 29-38, simplify and express answers using positive exponents only. Assume that variables are nonzero. 22+310In Problems 29-38, simplify and express answers using positive exponents only. Assume that variables are nonzero. 2x3y40In Problems 29-38, simplify and express answers using positive exponents only. Assume that variables are nonzero. 1031041011102In Problems 29-38, simplify and express answers using positive exponents only. Assume that variables are nonzero. 10171051031014In Problems 29-38, simplify and express answers using positive exponents only. Assume that variables are nonzero. 5x2y32In Problems 29-38, simplify and express answers using positive exponents only. Assume that variables are nonzero. 2m3n23In Problems 29-38, simplify and express answers using positive exponents only. Assume that variables are nonzero. 52x32In Problems 29-38, simplify and express answers using positive exponents only. Assume that variables are nonzero. 2a3b23In Problems 29-38, simplify and express answers using positive exponents only. Assume that variables are nonzero. 8x3y16x2y4In Problems 29-38, simplify and express answers using positive exponents only. Assume that variables are nonzero. 9m4n312m1n1In Problems 39-42, write each expression in the form axp+bxq or axp+bxq+cxr, where a, b, and c are real numbers and p, q, and r are integers. For example, 2x43x2+12x3=2x42x33x22x3+12x3=x32x1+12x3 7x5x24x5In Problems 39-42, write each expression in the form axp+bxq or axp+bxq+cxr, where a, b, and c are real numbers and p, q, and r are integers. For example, 2x43x2+12x3=2x42x33x22x3+12x3=x32x1+12x3 5x323x2In Problems 39-42, write each expression in the form axp+bxq or axp+bxq+cxr, where a, b, and c are real numbers and p, q, and r are integers. For example. 2x43x2+12x3=2x42x33x22x3+12x3=x32x1+12x3 5x43x2+82x2In Problems 39-42, write each expression in the form axp+bxq or axp+bxq+cxr, where a, b, and c are real numbers and p, q, and r are integers. For example. 2x43x2+12x3=2x42x33x22x3+12x3=x32x1+12x3 2x33x2+x2x2Write each expression in Problems 43-46 with positive exponents only, and as a single fraction reduced to lowest terms. 3x2x122x3x1x14Write each expression in Problems 43-46 with positive exponents only, and as a single fraction reduced to lowest terms. 5x4x+322x5x+3x+34Write each expression in Problems 43-46 with positive exponents only, and as a single fraction reduced to lowest terms. 2x2x12x3x12Write each expression in Problems 43-46 with positive exponents only, and as a single fraction reduced to lowest terms. 2xx+31x2x+32In Problems 47-50, convert each number to scientific notation and simplify. Express the answer in both scientific notation and in standard decimal form. 9,600,000,0001,600,0000.00000025In Problems 47-50, convert each number to scientific notation and simplify. Express the answer in both scientific notation and in standard decimal form. 60,0000.0000030.00041,500,000In Problems 47-50, convert each number to scientific notation and simplify. Express the answer in both scientific notation and in standard decimal form. 1,250,0000.000380.0152In Problems 47-50, convert each number to scientific notation and simplify. Express the answer in both scientific notation and in standard decimal form. 0.00000082230,000625,0000.0082What is the result of entering 232 on a calculator?Refer to Problem 51. What is the difference between 232 and 232 ? Which agrees with the value of 232 obtained with a calculator?In n=0, then property 1 in Theorem 1 implies that ama0=am+0=am. Explain how this helps motivate the definition of a0.In m=n, then property 1 in Theorem 1 implies that anan=a0=1. Explain how this helps motivate the definition of an.Write the fractions in Problems 55-58 as simple fractions reduced to lowest terms. u+vu1+v1Write the fractions in Problems 55-58 as simple fractions reduced to lowest terms. x2y2x1+y1Write the fractions in Problems 55-58 as simple fractions reduced to lowest terms. b2c2b3c3Write the fractions in Problems 55-58 as simple fractions reduced to lowest terms. xy2yx2y1x1Problems 59 and 60 refer to Table 1. Public debt. Carry out the following computations using scientific notation, and write final answers in standard decimal form. (A) What was the per capita debt in 2016 (to the nearest dollar)? (B) What was the per capita interest paid on the debt in 2016 (to the nearest dollar)? (C) What was the percentage interest paid on the debt in 2016 (to two decimal places) ?Problems 59 and 60 refer to Table 1. Public debt. Carry out the following computations using scientific notation, and write final answers in standard decimal form. (A) What was the per capita debt in 2000 (to the nearest What was the per capita debt in 2000 (to the nearest dollar)? (B) What was the per capita interest paid on the debt in 2000 (to the nearest dollar)? (C) What was the percentage interest paid on the debt in What was the percentage interest paid on the debt in 2000 (to two decimal places)?Air pollution. Air quality standards establish maximum amounts of pollutants considered acceptable in the air. The amounts are frequently given in parts per million (ppm). A standard of 30 ppm also can be expressed as follows: 30ppm=301,000,000=310106=3105=0.00003=0.003 In Problems 61 and 62. express the given standard: (A) In scientific notation (B) In standard decimal notation (C) As a percent 9 ppm, the standard for carbon monoxide, when averaged over a period of 8 hoursAir pollution. Air quality standards establish maximum amounts of pollutants considered acceptable in the air. The amounts are frequently given in parts per million (ppm). A standard of 30 ppm also can be expressed as follows: 30ppm=301,000,000=310106=3105=0.00003=0.003 In Problems 61 and 62. express the given standard: (A) In scientific notation (B) In standard decimal notation (C) As a percent 0.03 ppm, the standard for sulfur oxides, when averaged over a yearCrime. In 2015, the United States had a violent crime rate of 373 per 100,000 people and a population of 320 million people. How many violent crimes occurred that year? Compute the answer using scientific notation and convert the answer to standard decimal form (to the nearest thousand).Population density. The United States had a 2016 population of 323 million people and a land area of 3,539,000 square miles. What was the population density? Compute the answer using scientific notation and convert the answer to standard decimal form (to one decimal place).Evaluate each of the following: (A)161/2(B)16(C)273(D)91/2(E)8143Convert to radical form. (A)u1/5(B)6x2y52/9(C)3xy3/5 Convert to rational exponent form. (D)9u4(E)2x47(F)x3+y33Simplify each and express answers using positive exponents only. If rational exponents appear in final answers, convert to radical form. (A)93/2(B)274/3(C)5y1/42y1/3(D)2x3/4y1/44(E)8x1/2x2/31/3Multiply, and express answers using positive exponents only. (A)2c1/45c3c3/4(B)7x1/2y1/22x1/2+3y1/2Write the following expression in the form axp+bxq, where a and b are real numbers and p and q are rational numbers: 5x34x2x36MP7MPRationalize each numerator. (A)332(B)2n4n(C)3+h3hChange each expression in Problems 1-6 to radical form. Do not simplify. 6x3/5Change each expression in Problems 1-6 to radical form. Do not simplify. 7y2/5Change each expression in Problems 1-6 to radical form. Do not simplify. 32x2y33/5Change each expression in Problems 1-6 to radical form. Do not simplify. 7x2y5/7Change each expression in Problems 1-6 to radical form. Do not simplify. x2+y21/2Change each expression in Problems 1-6 to radical form. Do not simplify. x1/2+y1/27E8EChange each expression in Problems 7-12 to rational exponent form. Do not simplify. 2x2y3510EChange each expression in Problems 7-12 to rational exponent form. Do not simplify. x3+y3Change each expression in Problems 7-12 to rational exponent form. Do not simplify. x2+y33In Problems 13-24, find rational number representations for each, if they exist. 251/2In Problems 13-24, find rational number representations for each, if they exist. 641/3In Problems 13-24, find rational number representations for each, if they exist. 163/2In Problems 13-24, find rational number representations for each, if they exist. 163/4In Problems 13-24, find rational number representations for each, if they exist. 491/2In Problems 13-24, find rational number representations for each, if they exist. 491/2In Problems 13-24, find rational number representations for each, if they exist. 642/3In Problems 13-24, find rational number representations for each, if they exist. 642/3In Problems 13-24, find rational number representations for each, if they exist. 4253/2In Problems 13-24, find rational number representations for each, if they exist. 8272/3In Problems 13-24, find rational number representations for each, if they exist. 93/2