Intermediate Algebra
19th Edition
ISBN: 9780998625720
Author: Lynn Marecek
Publisher: OpenStax College
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Textbook Question
Chapter 5.2, Problem 174E
Use the Product Property for Exponents to explain why
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Assume {u1, U2, us} spans R³.
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Chapter 5 Solutions
Intermediate Algebra
Ch. 5.1 - Determine whether each polynomial is a monomial,...Ch. 5.1 - Determine whether each polynomial is a monomial,...Ch. 5.1 - Add or subtract: (a) 12q2+9q2 (b) 8mn3(5mn3) .Ch. 5.1 - Add or subtract: (a) 15c2+8c2 (b) 15y2z3(5y2z3) .Ch. 5.1 - Add: (a) 8y2+3z23y2 (b) m2n28m2+4n2 .Ch. 5.1 - Add: (a) 3m2+n27m2 (b) pq26p5q2 .Ch. 5.1 - Find the sum: (7x24x+5)+(x27x+3) .Ch. 5.1 - Find the sum: (14y2+6y4)+(3y2+8y+5) .Ch. 5.1 - Find the difference: (8x2+3x19)(7x214) .Ch. 5.1 - Find the difference: (9b25b4)(3b25b7) .
Ch. 5.1 - Subtract (a2+5ab6b2) from (a2+b2) .Ch. 5.1 - Subtract (m27mn3n2) from (m2+n2) .Ch. 5.1 - Find the sum: (3x24xy+5y2)+(2x2xy) .Ch. 5.1 - Find the sum: (2x23xy2y2)+(5x23xy) .Ch. 5.1 - Simplify: (x3x2y)(xy2+y3)+(x2y+xy2) .Ch. 5.1 - Simplify: (p3p2q)+(pq2+q3)(p2q+pq2) .Ch. 5.1 - For the function f(x)=3x2+2x15 , find (a) f(3) (b)...Ch. 5.1 - For the function g(x)=5x2x4 , find (a) g(2) (b)...Ch. 5.1 - The polynomial function h(t)=16t2+150 gives the...Ch. 5.1 - The polynomial function h(t)=16t2+175 gives the...Ch. 5.1 - For functions f(x)=2x24x+3 and g(x)=x22x6 , find...Ch. 5.1 - For functions f(x)=5x24x1 and g(x)=x2+3x+8 , find...Ch. 5.1 - In the following exercises, determine if the...Ch. 5.1 - In the following exercises, determine if the...Ch. 5.1 - In the following exercises, determine if the...Ch. 5.1 - In the following exercises, determine if the...Ch. 5.1 - In the following exercises, determine if the...Ch. 5.1 - In the following exercises, determine if the...Ch. 5.1 - In the following exercises, determine if the...Ch. 5.1 - In the following exercises, determine if the...Ch. 5.1 - In the following exercises, add or subtract the...Ch. 5.1 - In the following exercises, add or subtract the...Ch. 5.1 - In the following exercises, add or subtract the...Ch. 5.1 - In the following exercises, add or subtract the...Ch. 5.1 - In the following exercises, add or subtract the...Ch. 5.1 - In the following exercises, add or subtract the...Ch. 5.1 - In the following exercises, add or subtract the...Ch. 5.1 - In the following exercises, add or subtract the...Ch. 5.1 - In the following exercises, add or subtract the...Ch. 5.1 - In the following exercises, add or subtract the...Ch. 5.1 - In the following exercises, add or subtract the...Ch. 5.1 - In the following exercises, add or subtract the...Ch. 5.1 - In the following exercises, add or subtract the...Ch. 5.1 - In the following exercises, add or subtract the...Ch. 5.1 - In the following exercises, add or subtract the...Ch. 5.1 - In the following exercises, add or subtract the...Ch. 5.1 - In the following exercises, add or subtract the...Ch. 5.1 - In the following exercises, add or subtract the...Ch. 5.1 - In the following exercises, add or subtract the...Ch. 5.1 - In the following exercises, add or subtract the...Ch. 5.1 - In the following exercises, add or subtract the...Ch. 5.1 - In the following exercises, add or subtract the...Ch. 5.1 - In the following exercises, add or subtract the...Ch. 5.1 - In the following exercises, add or subtract the...Ch. 5.1 - In the following exercises, add the polynomials....Ch. 5.1 - In the following exercises, add the polynomials....Ch. 5.1 - In the following exercises, add the polynomials....Ch. 5.1 - In the following exercises, add the polynomials....Ch. 5.1 - In the following exercises, add the polynomials....Ch. 5.1 - In the following exercises, add the polynomials....Ch. 5.1 - In the following exercises, add the polynomials....Ch. 5.1 - In the following exercises, add the polynomials....Ch. 5.1 - In the following exercises, subtract the...Ch. 5.1 - In the following exercises, subtract the...Ch. 5.1 - In the following exercises, subtract the...Ch. 5.1 - In the following exercises, subtract the...Ch. 5.1 - In the following exercises, subtract the...Ch. 5.1 - In the following exercises, subtract the...Ch. 5.1 - In the following exercises, subtract the...Ch. 5.1 - In the following exercises, subtract the...Ch. 5.1 - In the following exercises, subtract the...Ch. 5.1 - In the following exercises, subtract the...Ch. 5.1 - In the following exercises, find the difference of...Ch. 5.1 - In the following exercises, find the difference of...Ch. 5.1 - In the following exercises, add the polynomials....Ch. 5.1 - In the following exercises, add the polynomials....Ch. 5.1 - In the following exercises, add the polynomials....Ch. 5.1 - In the following exercises, add the polynomials....Ch. 5.1 - In the following exercises, add or subtract the...Ch. 5.1 - In the following exercises, add or subtract the...Ch. 5.1 - In the following exercises, add or subtract the...Ch. 5.1 - In the following exercises, add or subtract the...Ch. 5.1 - In the following exercises, add or subtract the...Ch. 5.1 - In the following exercises, add or subtract the...Ch. 5.1 - In the following exercises, find the function...Ch. 5.1 - In the following exercises, find the function...Ch. 5.1 - In the following exercises, find the function...Ch. 5.1 - In the following exercises, find the function...Ch. 5.1 - In the following exercises, find the height for...Ch. 5.1 - In the following exercises, find the height for...Ch. 5.1 - In the following exercises, find the height for...Ch. 5.1 - In the following exercises, find the height for...Ch. 5.1 - In the following exercises, find the height for...Ch. 5.1 - In the following exercises, find the height for...Ch. 5.1 - In each example, find (a) (f+g)(x)(b) (f+g)(2)(c)...Ch. 5.1 - In each example, find (a) (f+g)(x)(b) (f+g)(2)(c)...Ch. 5.1 - In each example, find (a) (f+g)(x)(b) (f+g)(2)(c)...Ch. 5.1 - In each example, find (a) (f+g)(x)(b) (f+g)(2)(c)...Ch. 5.1 - Using your own words, explain the difference...Ch. 5.1 - Using your own words, explain the difference...Ch. 5.1 - Ariana thinks the sum 6y2+5y4 is 11y6. What is...Ch. 5.1 - Is every trinomial a second degree polynomial? If...Ch. 5.2 - Simplify each expression: (a) b9b8 (b) 42x4x (c)...Ch. 5.2 - Simplify each expression: (a) x12x4 (b) 1010x (c)...Ch. 5.2 - Simplify each expression: (a) x15x10 (b) 61465 (c)...Ch. 5.2 - Simplify each expression: (a) y43y37 (b) 1015107...Ch. 5.2 - Simplify each expression: (a) 110 (b) q0 .Ch. 5.2 - Simplify each expression: (a) 230 (b) r0 .Ch. 5.2 - Simplify each expression: (a)z3 (b) 107 (c) 1p8...Ch. 5.2 - Simplify each expression: (a) n2 (b) 104 (c) 1q7...Ch. 5.2 - Simplify each expression: (a) (23)4 (b) (mn)2 .Ch. 5.2 - Simplify each expression: (a) (35)3 (b) (ab)4 .Ch. 5.2 - Simplify each expression: (a) z4z5 (b)...Ch. 5.2 - Simplify each expression: (a) c8c7 (b)...Ch. 5.2 - Simplify each expression: (a) (b7)5 (b) (54)3 (c)...Ch. 5.2 - Simplify each expression: (a)(z6)9 (b) (37)7 (c)...Ch. 5.2 - Simplify each expression: (a) (2wx)5 (b) (11pq3)0...Ch. 5.2 - Simplify each expression: (a) (3y)3 (b) (8m2n3)0...Ch. 5.2 - Simplify each expression: (a) (p10)4 (b) (mn)7 (c)...Ch. 5.2 - Simplify each expression: (a) (2q)3 (b) (wx)4 (c)...Ch. 5.2 - Simplify each expression: (a) (c4d2)5(3cd5)4 (b) (...Ch. 5.2 - Simplify each expression: (a) (a3b2)6(4ab3)4 (b) (...Ch. 5.2 - Write in scientific notation: (a) 96,000 (b)...Ch. 5.2 - Write in scientific notation: (a) 48,300 (b)...Ch. 5.2 - Convert to decimal form: (a) 1.3103 (b) 1.2104 .Ch. 5.2 - Convert to decimal form: (a) 9.5104 (b) 7.5102 .Ch. 5.2 - Multiply or divide as indicated. Write answers in...Ch. 5.2 - Multiply or divide as indicated. Write answers in...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - In the following exercises, simplify each...Ch. 5.2 - 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In the following exercises, multiply or divide as...Ch. 5.2 - Use the Product Property for Exponents to explain...Ch. 5.2 - Jennifer thinks the quotient a24a6 simplifies to...Ch. 5.2 - Explain why 53=(5)3 but 54(5)4 .Ch. 5.2 - When you convert a number from decimal notation to...Ch. 5.3 - Multiply: (a) (5y7)(7y4) (b) (25a4b3)(15ab3) .Ch. 5.3 - Multiply: (a) (6b4)(9b5) (b) (23r5s)(12r6s7) .Ch. 5.3 - Multiply: (a) 3y(5y2+8y7) (b) 4x2y2(3x25xy+3y2) .Ch. 5.3 - Multiply: (a) 4x2(2x23x+5) (b) 6a3b(3a22ab+6b2) .Ch. 5.3 - Multiply: (a) (x+8)(x+9) (b) (3c+4)(5c2) .Ch. 5.3 - Multiply: (a) (5x+9)(4x+3) (b) (5y+2)(6y3) .Ch. 5.3 - Multiply: (a) (x7)(x+5) (b) (3x+7)(5x2) .Ch. 5.3 - Multiply: (a) (b3)(b+6) (b) (4y+5)(4y10) .Ch. 5.3 - Multiply: (a) (x2+6)(x8) (b) (2ab+5)(4ab4) .Ch. 5.3 - Multiply: (a) (y2+7)(y9) (b) (2xy+3)(4xy5) .Ch. 5.3 - Multiply using the Vertical Method: (5m7)(3m6) .Ch. 5.3 - Multiply using the Vertical Method: (6b5)(7b3) .Ch. 5.3 - Multiply (y3)(y25y+2) using (a) the Distributive...Ch. 5.3 - Multiply (x+4)(2x23x+5) using (a) the Distributive...Ch. 5.3 - Multiply: (a) (x+9)2 (b) (2cd)2 .Ch. 5.3 - Multiply: (a) (y+11)2 (b) (4x5y)2 .Ch. 5.3 - Multiply: (a) (6x+5)(6x5) (b) (4p7q)(4p+7q) .Ch. 5.3 - Multiply: (a) (2x+7)(2x7) (b) (3xy)(3x+y) .Ch. 5.3 - Choose the appropriate pattern and use it to find...Ch. 5.3 - Choose the appropriate pattern and use it to find...Ch. 5.3 - For functions f(x)=x5 and g(x)=x22x+3 , find (a)...Ch. 5.3 - For functions f(x7) and g(x)=x2+8x+4 , find (a)...Ch. 5.3 - In the following exercises, multiply the...Ch. 5.3 - In the following exercises, multiply the...Ch. 5.3 - In the following exercises, multiply the...Ch. 5.3 - In the following exercises, multiply the...Ch. 5.3 - In the following exercises, multiply. 182. (a)...Ch. 5.3 - In the following exercises, multiply. 183. (a)...Ch. 5.3 - In the following exercises, multiply. 184. (a)...Ch. 5.3 - In the following exercises, multiply. 185. (a)...Ch. 5.3 - In the following exercises, multiply the binomials...Ch. 5.3 - In the following exercises, multiply the binomials...Ch. 5.3 - In the following exercises, multiply the binomials...Ch. 5.3 - In the following exercises, multiply the binomials...Ch. 5.3 - In the following exercises, multiply the...Ch. 5.3 - In the following exercises, multiply the...Ch. 5.3 - In the following exercises, multiply the...Ch. 5.3 - In the following exercises, multiply the...Ch. 5.3 - In the following exercises, multiply the...Ch. 5.3 - In the following exercises, multiply the...Ch. 5.3 - In the following exercises, multiply the...Ch. 5.3 - In the following exercises, multiply the...Ch. 5.3 - In the following exercises, multiply the...Ch. 5.3 - In the following exercises, multiply the...Ch. 5.3 - In the following exercises, multiply the...Ch. 5.3 - In the following exercises, multiply the...Ch. 5.3 - In the following exercises, multiply the...Ch. 5.3 - In the following exercises, multiply the...Ch. 5.3 - In the following exercises, multiply the...Ch. 5.3 - In the following exercises, multiply the...Ch. 5.3 - In the following exercises, multiply using (a) the...Ch. 5.3 - In the following exercises, multiply using (a) the...Ch. 5.3 - In the following exercises, multiply using (a) the...Ch. 5.3 - In the following exercises, multiply using (a) the...Ch. 5.3 - In the following exercises, multiply using (a) the...Ch. 5.3 - In the following exercises, multiply using (a) the...Ch. 5.3 - In the following exercises, multiply. Use either...Ch. 5.3 - In the following exercises, multiply. Use either...Ch. 5.3 - In the following exercises, multiply. Use either...Ch. 5.3 - In the following exercises, multiply. Use either...Ch. 5.3 - In the following exercises, square each binomial...Ch. 5.3 - In the following exercises, square each binomial...Ch. 5.3 - In the following exercises, square each binomial...Ch. 5.3 - In the following exercises, square each binomial...Ch. 5.3 - In the following exercises, square each binomial...Ch. 5.3 - In the following exercises, square each binomial...Ch. 5.3 - In the following exercises, square each binomial...Ch. 5.3 - In the following exercises, square each binomial...Ch. 5.3 - In the following exercises, square each binomial...Ch. 5.3 - In the following exercises, square each binomial...Ch. 5.3 - In the following exercises, square each binomial...Ch. 5.3 - In the following exercises, square each binomial...Ch. 5.3 - In the following exercises, multiply each pair of...Ch. 5.3 - In the following exercises, multiply each pair of...Ch. 5.3 - In the following exercises, multiply each pair of...Ch. 5.3 - In the following exercises, multiply each pair of...Ch. 5.3 - In the following exercises, multiply each pair of...Ch. 5.3 - In the following exercises, multiply each pair of...Ch. 5.3 - In the following exercises, multiply each pair of...Ch. 5.3 - In the following exercises, multiply each pair of...Ch. 5.3 - In the following exercises, multiply each pair of...Ch. 5.3 - In the following exercises, multiply each pair of...Ch. 5.3 - In the following exercises, multiply each pair of...Ch. 5.3 - In the following exercises, multiply each pair of...Ch. 5.3 - In the following exercises, find each product....Ch. 5.3 - In the following exercises, find each product....Ch. 5.3 - In the following exercises, find each product....Ch. 5.3 - In the following exercises, find each product....Ch. 5.3 - In the following exercises, find each product....Ch. 5.3 - In the following exercises, find each product....Ch. 5.3 - In the following exercises, find each product....Ch. 5.3 - In the following exercises, find each product....Ch. 5.3 - In the following exercises, find each product....Ch. 5.3 - In the following exercises, find each product....Ch. 5.3 - In the following exercises, find each product....Ch. 5.3 - In the following exercises, find each product....Ch. 5.3 - In the following exercises, find each product....Ch. 5.3 - In the following exercises, find each product....Ch. 5.3 - In the following exercises, find each product....Ch. 5.3 - In the following exercises, find each product....Ch. 5.3 - (10y6)+(4y7)Ch. 5.3 - (15p4)+(3p5)Ch. 5.3 - (x24x34)(x2+7x6)Ch. 5.3 - (j28j27)(j2+2j12)Ch. 5.3 - (15f8)(20f3)Ch. 5.3 - (14d5)(36d2)Ch. 5.3 - (4a3b)(9a2b6)Ch. 5.3 - (6m4n3)(7mn5)Ch. 5.3 - 5m(m2+3m18)Ch. 5.3 - 5q3(q22q+6)Ch. 5.3 - (s7)(s+9)Ch. 5.3 - (y22y)(y+1)Ch. 5.3 - (5xy)(x4)Ch. 5.3 - (6k1)(k2+2k4)Ch. 5.3 - (3x11y)(3x11y)Ch. 5.3 - (11b)(11+b)Ch. 5.3 - (rs27)(rs+27)Ch. 5.3 - (2x23y4)(2x2+3y4)Ch. 5.3 - (m15)2Ch. 5.3 - (3d+1)2Ch. 5.3 - (4a+10)2Ch. 5.3 - (3z+15)2Ch. 5.3 - For functions f(x)=x+2 and g(x)=3x22x+4 , find (a)...Ch. 5.3 - For functions f(x)=x1 and g(x)=4x2+3x5 , find (a)...Ch. 5.3 - For functions f(x)=2x7 and g(x)=2x+7 , find (a)...Ch. 5.3 - For functions f(x)=7x8 and g(x)=7x+8 , find (a)...Ch. 5.3 - For functions f(x)=x25x+2 and g(x)=x23x1 , find...Ch. 5.3 - For functions f(x)=x2+4x3 and g(x)=x2+2x+4 , find...Ch. 5.3 - Which method do you prefer to use when multiplying...Ch. 5.3 - Multiply the following:...Ch. 5.3 - Multiply the following:...Ch. 5.3 - Why does (a+b)2 result in a trinomial, but...Ch. 5.4 - Find the quotient: 72a7b3(8a12b4) .Ch. 5.4 - Find the quotient: 63c8d3(7c12d2) .Ch. 5.4 - Find the quotient: 28x5y1449x9y12 .Ch. 5.4 - Find the quotient: 30m5n1148m10n14 .Ch. 5.4 - Find the quotient: (32a2b16ab2)(8ab) .Ch. 5.4 - Find the quotient: (48a8b436a6b5)(6a3b3) .Ch. 5.4 - Find the quotient: (y2+10y+21)(y+3) .Ch. 5.4 - Find the quotient: (m2+9m+20)(m+4) .Ch. 5.4 - Find the quotient: (x47x2+7x+6)(x+3) .Ch. 5.4 - Find the quotient: (x411x27x6)(x+3) .Ch. 5.4 - Find the quotient: (x264)(x4) .Ch. 5.4 - Find the quotient: (125x38)(5x2) .Ch. 5.4 - Use synthetic division to find the quotient and...Ch. 5.4 - Use synthetic division to find the quotient and...Ch. 5.4 - Use synthetic division to find the quotient and...Ch. 5.4 - Use synthetic division to find the quotient and...Ch. 5.4 - For functions f(x)=x25x24 and g(x)=x+3 , find (a)...Ch. 5.4 - For functions f(x)=x25x36 and g(x)=x+4 , find (a)...Ch. 5.4 - Use the Remainder Theorem to find the remainder...Ch. 5.4 - Use the Remainder Theorem to find the remainder...Ch. 5.4 - Use the Factor Theorem to determine if x5 is a...Ch. 5.4 - Use the Factor Theorem to determine if x6 is a...Ch. 5.4 - In the following exercises, divide the monomials....Ch. 5.4 - In the following exercises, divide the monomials....Ch. 5.4 - In the following exercises, divide the monomials....Ch. 5.4 - In the following exercises, divide the monomials....Ch. 5.4 - In the following exercises, divide the monomials....Ch. 5.4 - In the following exercises, divide the monomials....Ch. 5.4 - In the following exercises, divide the monomials....Ch. 5.4 - In the following exercises, divide the monomials....Ch. 5.4 - In the following exercises, divide each polynomial...Ch. 5.4 - In the following exercises, divide each polynomial...Ch. 5.4 - In the following exercises, divide each polynomial...Ch. 5.4 - In the following exercises, divide each polynomial...Ch. 5.4 - In the following exercises, divide each polynomial...Ch. 5.4 - In the following exercises, divide each polynomial...Ch. 5.4 - In the following exercises, divide each polynomial...Ch. 5.4 - In the following exercises, divide each polynomial...Ch. 5.4 - In the following exercises, divide each polynomial...Ch. 5.4 - In the following exercises, divide each polynomial...Ch. 5.4 - In the following exercises, divide each polynomial...Ch. 5.4 - In the following exercises, divide each polynomial...Ch. 5.4 - In the following exercises, divide each polynomial...Ch. 5.4 - In the following exercises, divide each polynomial...Ch. 5.4 - In the following exercises, divide each polynomial...Ch. 5.4 - In the following exercises, divide each polynomial...Ch. 5.4 - In the following exercises, divide each polynomial...Ch. 5.4 - In the following exercises, divide each polynomial...Ch. 5.4 - In the following exercises, divide each polynomial...Ch. 5.4 - In the following exercises, divide each polynomial...Ch. 5.4 - In the following exercises, use synthetic Division...Ch. 5.4 - In the following exercises, use synthetic Division...Ch. 5.4 - In the following exercises, use synthetic Division...Ch. 5.4 - In the following exercises, use synthetic Division...Ch. 5.4 - In the following exercises, use synthetic Division...Ch. 5.4 - In the following exercises, use synthetic Division...Ch. 5.4 - In the following exercises, use synthetic Division...Ch. 5.4 - In the following exercises, use synthetic Division...Ch. 5.4 - In the following exercises, divide. 324. 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