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All Textbook Solutions for PREALGEBRA
Simplify: a.(8)2 b. 82Simplify:x7.x8.Simplify: x5.x11Simplify:p9.p.Simplify:m.m7Simplify:6.69Simplify: 96.99Simplify: y24.y19Simplify: z15.z24Simplify: x7.x5.x9Simplfy: y3.y8.y4.Simplify: a. (x7)4 b. (74)8Simplify: (x6)9 (86)7Simplify (14x)2Simplify: (12a)2Simplify: (4xy)4Simplfy: (6xy)3Simplify: (x4)3(x7)4.Simplify: (y9)2(y8)3Simplify: (8x4y7)3.Simplify: (3a5b6)4.Simplify: (7n)2(2n12).Simplify: (4m2)(3m3).Simplify (u3v2)(4uv4)3.Simplify: (5x2y3)2(3xy4)3Simplify: sw (7x7)(8x4).Mulitiply: (9y4)(6y5)Multiply: (45m4n3) (15mn3)Multiply: (23p5q)(18p6q7)Simplify Expressions with Exponents In the following exercises, simplify each expression with exponents. 45Simplify Expressions with Exponents In the following exercises, simplify each expression with exponents. 103Simplify Expressions with Exponents In the following exercises, simplify each expression with exponents. (12)2Simplify Expressions with Exponents In the following exercises, simplify each expression with exponents. (35)2Simplify Expressions with Exponents In the following exercises, simplify each expression with exponents. (0.2)3Simplify Expressions with Exponents In the following exercises, simplify each expression with exponents. (0.4)3Simplify Expressions with Exponents In the following exercises, simplify each expression with exponents. (5)4Simplify Expressions with Exponents In the following exercises, simplify each expression with exponents. (3)5Simplify Expressions with Exponents In the following exercises, simplify each expression with exponents. 54Simplify Expressions with Exponents In the following exercises, simplify each expression with exponents. 35Simplify Expressions with Exponents In the following exercises, simplify each expression with exponents. 104Simplify Expressions with Exponents In the following exercises, simplify each expression with exponents. 26Simplify Expressions with Exponents In the following exercises, simplify each expression with exponents. (23)3Simplify Expressions with Exponents In the following exercises, simplify each expression with exponents. (14)4Simplify Expressions with Exponents In the following exercises, simplify each expression with exponents. 0.52Simplify Expressions with Exponents In the following exercises, simplify each expression with exponents. 0.14Simplify Expressions Using the Product Property of Exponents In the following exercises, simplify each expression using the Product Property of Exponents. x3x6Simplify Expressions Using the Product Property of Exponents In the following exercises, simplify each expression using the Product Property of Exponents. m4m2Simplify Expressions Using the Product Property of Exponents In the following exercises, simplify each expression using the Product Property of Exponents. aa4Simplify Expressions Using the Product Property of Exponents In the following exercises, simplify each expression using the Product Property of Exponents. y12ySimplify Expressions Using the Product Property of Exponents In the following exercises, simplify each expression using the Product Property of Exponents. 3539Simplify Expressions Using the Product Property of Exponents In the following exercises, simplify each expression using the Product Property of Exponents. 51056Simplify Expressions Using the Product Property of Exponents In the following exercises, simplify each expression using the Product Property of Exponents. zz2z3Simplify Expressions Using the Product Property of Exponents In the following exercises, simplify each expression using the Product Property of Exponents. aa3a5Simplify Expressions Using the Product Property of Exponents In the following exercises, simplify each expression using the Product Property of Exponents. xax2Simplify Expressions Using the Product Property of Exponents In the following exercises, simplify each expression using the Product Property of Exponents. ypy3Simplify Expressions Using the Product Property of Exponents In the following exercises, simplify each expression using the Product Property of Exponents. yaybSimplify Expressions Using the Product Property of Exponents In the following exercises, simplify each expression using the Product Property of Exponents. xpxqSimplify Expressions Using the Power Property of Exponents In the following exercises, simplify each expression using the Power Property of Exponents. (u4)2Simplify Expressions Using the Power Property of Exponents In the following exercises, simplify each expression using the Power Property of Exponents. (x2)7Simplify Expressions Using the Power Property of Exponents In the following exercises, simplify each expression using the Power Property of Exponents. (y5)4Simplify Expressions Using the Power Property of Exponents In the following exercises, simplify each expression using the Power Property of Exponents. (a3)2Simplify Expressions Using the Power Property of Exponents In the following exercises, simplify each expression using the Power Property of Exponents. (102)6Simplify Expressions Using the Power Property of Exponents In the following exercises, simplify each expression using the Power Property of Exponents. (28)3Simplify Expressions Using the Power Property of Exponents In the following exercises, simplify each expression using the Power Property of Exponents. (x15)6Simplify Expressions Using the Power Property of Exponents In the following exercises, simplify each expression using the Power Property of Exponents. (y12)8Simplify Expressions Using the Power Property of Exponents In the following exercises, simplify each expression using the Power Property of Exponents. (x2)ySimplify Expressions Using the Power Property of Exponents In the following exercises, simplify each expression using the Power Property of Exponents. (y3)xSimplify Expressions Using the Power Property of Exponents In the following exercises, simplify each expression using the Power Property of Exponents. (5x)ySimplify Expressions Using the Power Property of Exponents In the following exercises, simplify each expression using the Power Property of Exponents. (7a)bSimplify Expressions Using the Product to a Power Property In the following exercises, simplify each expression using the Product to a Power Property. (5a)2Simplify Expressions Using the Product to a Power Property In the following exercises, simplify each expression using the Product to a Power Property. (7x)2Simplify Expressions Using the Product to a Power Property In the following exercises, simplify each expression using the Product to a Power Property. (6m3)Simplify Expressions Using the Product to a Power Property In the following exercises, simplify each expression using the Product to a Power Property. (9n)3Simplify Expressions Using the Product to a Power Property In the following exercises, simplify each expression using the Product to a Power Property. (4rs)2Simplify Expressions Using the Product to a Power Property In the following exercises, simplify each expression using the Product to a Power Property. (5ab)3Simplify Expressions Using the Product to a Power Property In the following exercises, simplify each expression using the Product to a Power Property. (4xyz)4Simplify Expressions Using the Product to a Power Property In the following exercises, simplify each expression using the Product to a Power Property. (5abc)3Simplify Expressions by Applying Several Properties In the following exercises, simplify each expression. (x2)4(x3)2Simplify Expressions by Applying Several Properties In the following exercises, simplify each expression. (y4)3(y5)2Simplify Expressions by Applying Several Properties:In the following exercises, simplify each expression. (a2)6(a3)8Simplify Expressions by Applying Several Properties In the following exercises, simplify each expression. (b7)5(b2)6Simplify Expressions by Applying Several Properties In the following exercises, simplify each expression. (3x)2(5x)Simplify Expressions by Applying Several Properties In the following exercises, simplify each expression. (2y)3(6y)Simplify Expressions by Applying Several Properties In the following exercises, simplify each expression. (5a)2(2a)3Simplify Expressions by Applying Several Properties In the following exercises, simplify each expression. (4b)2(3b)3Simplify Expressions by Applying Several Properties In the following exercises, simplify each expression. (2m6)3Simplify Expressions by Applying Several Properties In the following exercises, simplify each expression. (3y2)4Simplify Expressions by Applying Several Properties In the following exercises, simplify each expression. (10x2y)3Simplify Expressions by Applying Several Properties In the following exercises, simplify each expression. . (2mn4)5Simplify Expressions by Applying Several Properties In the following exercises, simplify each expression. (2a3b2)4Simplify Expressions by Applying Several Properties In the following exercises, simplify each expression. (10u2v4)3Simplify Expressions by Applying Several Properties In the following exercises, simplify each expression. (23x2y)3Simplify Expressions by Applying Several Properties In the following exercises, simplify each expression. (79pq4)2Simplify Expressions by Applying Several Properties In the following exercises, simplify each expression. (8a3)2(2a)4Simplify Expressions by Applying Several Properties In the following exercises, simplify each expression. (5r2)3(3r)2Simplify Expressions by Applying Several Properties In the following exercises, simplify each expression. (10p4)3(5p6)2Simplify Expressions by Applying Several Properties In the following exercises, simplify each expression. (4x3)3(2x5)4Simplify Expressions by Applying Several Properties In the following exercises, simplify each expression. (12x2y3)4(4x5y3)2Simplify Expressions by Applying Several Properties In the following exercises, simplify each expression. (13m3n2)4(9m8n3)2Simplify Expressions by Applying Several Properties In the following exercises, simplify each expression. (3m2n)2(2mn5)4Simplify Expressions by Applying Several Properties In the following exercises, simplify each expression. (2pq4)3(5p6q)2Multiply Monomials In the following exercises, multi ply the following monomials. (12x2)(5x4)Multiply Monomials In the following exercises, multi ply the following monomials. (10y3)(7y2)Multiply Monomials In the following exercises, multi ply the following monomials. (8u6)(9u)Multiply Monomials In the following exercises, multi ply the following monomials. (6c4)(12c)Multiply Monomials In the following exercises, multiply the following monomials. (15r8)(20r3)Multiply Monomials In the following exercises, multi ply the following monomials. (14a5)(36a2)Multiply Monomials In the following exercises, multi ply the following monomials. (4a3b)(9a2b6)Multiply Monomials In the following exercises, multi ply the following monomials. (6m4n3)(7mn5)Multiply Monomials In the following exercises, multiply the following monomials. (47xy2)(14xy3)Multiply Monomials In the following exercises, multiply the following monomials. (58u3v)(24u5v)Multiply Monomials In the following exercises, multiply the following monomials. (23x2y)(34xy2)Multiply Monomials In the following exercises, multiply the following monomials. (35m3n2)(59m2n3)Email Janet emails a joke to six of her friends and tells them to forward it to six of their friends, who forward it to six of their friends, and so on. The number of people who receive the email on the second round is 62, on the third round is 6, as shown in the table. How many people will receive the email on the eighth round? Simplify the expression to show the number of people who receive the email. Round Number of people 1 1 6 2 62 3 6 8 ?Salary Raul’s boss gives him a 5% raise every year on his birthday. This means that each year, Raul’s salary is 1.05 times his last year’s salary. If his original salary was S40.000, his salary after 1 year was $40.000(1.05), after 2 years was $4.O000(1.05)2, after 3 years was $40.000(1.05)3. as shown in the table below. What will Raul’s salary be after 10 years? Simplify the expression, to show Raul’s salary in dollars. Year Salary 1 $40,000(1,05) 2 3 … … 10 ?Use the Product Property for Exponents to explain why x.x=x2Explain why 53=(5)3but 54(5)4.Jorge thinks (12)2is 1. What is wrong with his reasoning?Explain why x3.x5is x8, and not x15..Multiply: 6(x+8)Multiply: 2(y+12)Multiply: y(y9)Multiply: p(p13)Multiply: 8x(3x+3y)Multiply: 3r(6r+s)Multiply: 4y(8y2+5y9).Multiply: 6x(9x2+x1).Multiply: 3x2(4x23x+9)Multiply: 8y2(3y22y4)Multiply: (x+8)p.Multiply: (a+4)pMultiply: (x+8)(x+9).Multiply: (q4)(q+5).Multiply: (5x+9)(4x+3).Multiply: (10m+9)(8m+7).Multiply: (7y+1) (8y3)Multiply: (3x+2)(5x8).Multiply: . (x+5)(xy)Multiply: (x+2y)(x1)Multiply using the FOIL method: (x + 7)(x + 8).Multiply using the FOIL method: (y+14)(y+2)Multiply: (y3)(y+8)Multiply: (q4)(q+5).Multiply: (4a9)(5a2)Multiply: (7x+4)(7x8).Multiply: (12xy)(x5)Multiply: (6ab)(2a9)Multiply using the vertical method: (4m9)(3m7).Multiply using the vertical method: (6n5)(7n2).Multiphy using the Distributive Property: (y1)(y27y+2)Multiply using the Distributive Property (x+2)(3x24x+5).Multiply using the Vertical Method: (y1)(y27y+2).Multiply using the Vertical Method: (x+2)(3x24x+5).Multiply a Polynomial by a Monomial In the following exercises, multiply. 4(x+10)Multiply a Polynomial by a Monomial In the following exercises, multiply. 6(y+8)Multiply a Polynomial by a Monomial In the following exercises, multiply. 15(r24)Multiply a Polynomial by a Monomial In the following exercises, multiply. 12(v30)Multiply a Polynomial by a Monomial In the following exercises, multiply. 3(m+11)Multiply a Polynomial by a Monomial In the following exercises, multiply. 4(q+15)Multiply a Polynomial by a Monomial In the following exercises, multiply. 8(z5)Multiply a Polynomial by a Monomial In the following exercises, multiply. 3(x9)Multiply a Polynomial by a Monomial In the following exercises, multiply. u(u+5)Multiply a Polynomial by a Monomial In the following exercises, multiply. q(q+7)Multiply a Polynomial by a Monomial In the following exercises, multiply. n(n23n)Multiply a Polynomial by a Monomial In the following exercises, multiply. s(s26s)Multiply a Polynomial by a Monomial In the following exercises, multiply. 12x(x10)Multiply a Polynomial by a Monomial In the following exercises, multiply. 9m(m1)Multiply a Polynomial by a Monomial In the following exercises, multiply. 9a(3a+5)Multiply a Polynomial by a Monomial In the following exercises, multiply. 4p(2p+7)Multiply a Polynomial by a Monomial In the following exercises, multiply. 6x(4x+y)Multiply a Polynomial by a Monomial In the following exercises, multiply. 5a(9a+b)Multiply a Polynomial by a Monomial In the following exercises, multiply. 5p(11p5q)Multiply a Polynomial by a Monomial In the following exercises, multiply. 12u(3u4v)Multiply a Polynomial by a Monomial In the following exercises, multiply. 3(v2+10v+25)Multiply a Polynomial by a Monomial In the following exercises, multiply. 6(x2+8x+16)Multiply a Polynomial by a Monomial In the following exercises, multiply. 2n(4n24n+1)Multiply a Polynomial by a Monomial In the following exercises, multiply. 3r(2x26r+2)Multiply a Polynomial by a Monomial In the following exercises, multiply. 8y(y2+2y15)Multiply a Polynomial by a Monomial In the following exercises, multiply. 5m(m2+3m18)Multiply a Polynomial by a Monomial In the following exercises, multiply. 5q3(q22q+6)Multiply a Polynomial by a Monomial In the following exercises, multiply. 9r3(r13r+5)Multiply a Polynomial by a Monomial In the following exercises, multiply. 4z2(3z2+12z1)Multiply a Polynomial by a Monomial In the following exercises, multiply. 3x2(7x2+10x1)Multiply a Polynomial by a Monomial In the following exercises, multiply. (2y9)yMultiply a Polynomial by a Monomial In the following exercises, multiply. (8b1)bMultiply a Polynomial by a Monomial In the following exercises, multiply. (w6)8Multiply a Polynomial by a Monomial In the following exercises, multiply. (k4)5Multiply a Binomial by a Binomial In the following exercises. multip4’ the following binomials using: a. the Distributive Property b. the FOIL method c. the Vertical method (x+4)(x+6)Multiply a Binomial by a Binomial In the following exercises. multip4’ the following binomials using: a. the Distributive Property b. the FOIL method c. the Vertical method (u+8)(u+2)Multiply a Binomial by a Binomial In the following exercises. multiply the following binomials using: a. the Distributive Property b. the FOIL method c. the Vertical method (n+12)(n3)Multiply a Binomial by a Binomial In the following exercises. multip4’ the following binomials using: a. the Distributive Property b. the FOIL method c. the Vertical method (y+3)(y9)In the following exercises, multiply the following binomials, Use any method. (y+8)(y+3)In the following exercises, multiply the following binomials. Use any method. (x+5)(x+9)In the following exercises, multiply the following binomials. Use any method. (a+6)(a+16)In the following exercises, multiply the following binomials. Use any method. (q+8)(q+12)In the following exercises, multiply the following binomials. Use any method. (u5)(u9)In the following exercises, multiply the following binomials, Use any method. (r6)(r2)In the following exercises, multiply the following binomials. Use any method. (z10)(z22)In the following exercises, multiply the following binomials. Use any method. (b5)(b24)In the following exercises, multiply the following binomials. Use any method. (x4)(x+7)In the following exercises, multiply the following binomials. Use any method. (s3)(s+8)In the following exercises, multiply the following binomials. Use any method. (v+12)(v5)In the following exercises, multiply the following binomials, Use any method. (d+15)(d4)In the following exercises, multiply the following binomials. Use any method. (6n+5)(n+1)In the following exercises, multiply the following binomials. Use any method. (7y+1)(y+3)In the following exercises, multiply the following binomials. Use any method. (2m9)(10m+1)In the following exercises, multiply the following binomials. Use any method. (5r4)(12r+1)In the following exercises, multiply the following binomials. Use any method. (4c1)(4c+1)In the following exercises, multiply the following binomials. Use any method. (8n1)(8n+1)In the following exercises, multiply the following binomials, Use any method. (3u8)(5u14)In the following exercises, multiply the following binomials. Use any method. (2q5)(7q11)In the following exercises, multiply the following binomials. Use any method. (a+b)(2a+3b)In the following exercises, multiply the following binomials. Use any method. (r+s)(3r+2s)In the following exercises, multiply the following binomials. Use any method. (5xy)(x4)In the following exercises, multiply the following binomials. Use any method. (4zy)(z6)Multiply a Trinomial by a Binomial In the following exercises, multiply using a. the Distributive Property and b. the Vertical Method. (u+4)(u2+3u+2)Multiply a Trinomial by a Binomial In the following exercises, multiply using a. the Distributive Property and b. the Vertical Method. (x+5)(x2+8x+3)Multiply a Trinomial by a Binomial In the following exercises. Multiply using a. the Distributive Property and b. the Vertical Method. (a+10)(3a2+a5)Multiply a Trinomial by a Binomial In the following exercises, multiply using a. the Distributive Property and b. the Vertical Method. (n+8)(4n2+n7)In the following exercises, multiply. Use either method. (y6)(y210y+9)In the following exercises, multiply. Use either method. (k3)(k28k+7)In the following exercises, multiply. Use either method. (2x+1)(x25x6)In the following exercises, multiply. Use either method. (5v+1)(v26v10)Mental math You can use binomial multiplication to multiply numbers without a calculator. Say you need to multiply 13 times 15. Think of 13 as 10+3 and 15 as 10+5. 0 Multiply (10 + 3)(1O+ 5) by the FOIL method. ® Multiply 13.15 without using a calculator. 0 Which way is easier for you? Why?Mental math You can use binomial multiplication to multiply numbers without a calculator. Say you need to multiply 18 times 17. Think of 18 as 20 — 2 and 17 as 20 —3. a. Multiply (20 -2)(20 — 3) by the FOIL method. b. Multiply 18. 17 without using a calculator. c. Which way is easier for you’ Why?Which method do you prefer to use when multiplying two binomials—the Distributive Property, the FOIL method, or the Vertical Method? Why?Which method do you prefer to use when multiplying a trinomial by a binomial—the Distributive Property or the Vertical Method? Why?Simplify: a. x12x9 b. 71475Simplify: y23y17 81587Simplify: x8x15 12111221Simplify: a.m17m26 b. 78714Simplify: b19b11 z4z11Simplify: p9p17 w12w9Simplify: 170 m0Simplify: a. k0 b. 290Simplify: (4y)0Simplify: (23x)0.Simplify: a. (7x2y)0 b. 7x2y0Simplify: a. 23x2y0 b. (23x2y)0Simplify: (79)2 (y9)3 (pq)6Simplify: (18)2 (5m)3 (rs)4Simplify: (a4)5a9Simplify: (b5)6b11Simplify: k11(k3)3Simplify: d12(d4)5.Simplify: (f14f9)2ZSimplify: (b6b11)2Simplify: (m3n8)5Simplify: (t10u7)2.Simplify: (5b9c3)2.Simplify: (4p47q5)3.Simplify: (y4)4(y3)5(y7)6Simplify: (3x4)4(x3)4(x5)3Find the quotient: 63x89x4Find the quotient: 96y11+6y8.Find the quotient: 84x8y37x10y2Find the qutionient: 72a4b58a9b5Find the quotient: 16a7b624ab8Find the quotient: 27p4q745p12q.Find the quotient: 28x5y1449x9y12Find the quotient: 30m5n1148m10n14Find the quotient: (3x4y5)(8x2y4)12x5y8Find the quotient: (6a6b9)(8a5b8)12a10b12.Simplify Expressions Using the Quotient Property of Exponents In the following exercises, simplify. 4842Simplify Expressions Using the Quotient Property of Exponents In the following exercises, simplify. 31234Simplify Expressions Using the Quotient Property of Exponents In the following exercises, simplify. x12x3Simplify Expressions by Applying Several Properties In the following exercises, simplify u9u3Simplify Expressions Using the Quotient Property of Exponents In the following exercises, simplify. r4rSimplify Expressions Using the Quotient Property of Exponents In the following exercises, simplify. y4ySimplify Expressions Using the Quotient Property of Exponents In the following exercises, simplify. y4y20Simplify Expressions Using the Quotient Property of Exponents In the following exercises, simplify. x10x30Simplify Expressions Using the Quotient Property of Exponents In the following exercises, simplify. 1031015Simplify Expressions Using the Quotient Property of Exponents In the following exercises, simplify. r2r8Simplify Expressions Using the Quotient Property of Exponents In the following exercises, simplify. aa9Simplify Expressions Using the Quotient Property of Exponents In the following exercises, simplify. 225Simplify Expressions with Zero Exponents In the following exercises, simplify. 50Simplify Expressions with Zero Exponents In the following exercises, simplify. 100Simplify Expressions with Zero Exponents In the following exercises, simplify. a0Simplify Expressions with Zero Exponents In the following exercises, simplify. x0Simplify Expressions with Zero Exponents In the following exercises, simplify. 70Simplify Expressions with Zero Exponents In the following exercises, simplify. 40Simplify Expressions with Zero Exponents In the following exercises, simplify. a. (10p)0 b. 10p0Simplify Expressions with Zero Exponents In the following exercises, simplify. a. (3a)0 b. 3a0Simplify Expressions with Zero Exponents In the following exercises, simplify. a. (27x5y)0 b. 27x5y0Simplify Expressions with Zero Exponents In the following exercises, simplify. a. (92y8z)0 b. 92y8z0Simplify Expressions with Zero Exponents In the following exercises, simplify. a. 150 b. 151Simplify Expressions with Zero Exponents In the following exercises, simplify. a. 60 b. 61Simplify Expressions with Zero Exponents In the following exercises, simplify. 2x0+5y0Simplify Expressions with Zero Exponents In the following exercises, simplify. 8m04n0Simplify Expressions Using the Quotient to a Power Property In the following exercises, simplify. (32)5Simplify Expressions Using the Quotient to a Power Property In the following exercises, simplify. (45)3Simplify Expressions Using the Quotient to a Power Property In the following exercises, simplify. (m6)3Simplify Expressions Using the Quotient to a Power Property In the following exercises, simplify. (p2)5Simplify Expressions Using the Quotient to a Power Property In the following exercises, simplify. (xy)10Simplify Expressions Using the Quotient to a Power Property In the following exercises, simplify. (ab)8Simplify Expressions Using the Quotient to a Power Property In the following exercises, simplify. (a3b)2Simplify Expressions Using the Quotient to a Power Property In the following exercises, simplify. (2xy)4Simplify Expressions by Applying Several Properties In the following exercises, simplify. (x2)4x5Simplify Expressions by Applying Several Properties In the following exercises, simplify. (y4)3y7Simplify Expressions by Applying Several Properties In the following exercises, simplify. (u3)4u10