1. Chapter 5 Exponents and Polynomials
5.1 Rules for exponents 5.2 Negative Exponents and Scientific Notation 5.3 Adding and Subtracting Polynomials 5.4 Multiplying Polynomials 5.5 Dividing Polynomials

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Simplify each exponential expression. a. 53 b. (–5)2 c. –52 d. (–g)2
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5.1-1

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Simplify each expression, using the product rule for exponents. a. r3r4 b. 23 · 25 c. x5x
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5.1-2

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Simplify each expression. a. (4a3b5)(3a7b2) b. (–5x4y3)(4x2y)
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5.1-3

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Simplify each expression, using the quotient rule for exponents. a. b.
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5.1-4ab

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Simplify each expression, using the quotient rule for exponents. c.
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5.1-4c

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Simplify each expression, using the product or quotient rule for exponents or both. a. b. c.
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5.1-5

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Simplify each expression, using the power rule for exponents. a. (x4)3 b. (23)4
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5.1-6

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Simplify each expression. a. b. c.
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5.1-7

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Simplify each expression. a. b.
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5.1-8ab

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Simplify each expression. c. d.
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5.1-8cd

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Rewrite without negative exponents. a. b.
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5.2-1ab

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Rewrite without negative exponents. c. d.
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5.2-1cd

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Simplify. Write the final answer using positive exponents only. a. b.
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5.2-2ab

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Simplify. Write the final answer using positive exponents only. c. d.
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5.2-2cd

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Convert the following numbers into scientific notation. a. Microsoft Corporation market capitalization on April 1, 2010: $256,000,000,000. b. The wavelength of a certain light: meter.
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5.2-3

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Perform the indicated operation. Write the answer in scientific notation. a. b. c.
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5.2-4

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The elementary charge, the electric charge carried by a single proton, is approximately × 10–19 coulomb. Find the electric charge of 800 protons.
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5.2-5

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Perform the indicated operation. Write the answer in scientific notation. a. (7.0 × 108)(2.3 × 1011) b. (3.6 × 10–9)(2.3 × 10–7) c.
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5.2-6

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The mass of the sun is estimated at 1.99 × 1030 kg, and the mass of the earth is 5.98 × 1024 kg. Divide the mass of the sun by the mass of the earth to find how much larger the mass of the sun is than that of the earth.
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5.2-7

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Identify the terms in each of the following polynomials. Label the polynomial as a monomial, binomial, or trinomial. a. 8x2 + 7x – 10 b. 8a + 28 c. 47m5n3
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5.3-1

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For the given polynomials, list the degree of the polynomial. Rewrite the polynomial in descending order. a. x4 + 8x2 – 9 b. 6x – 7 + 2x5 + x3 c.
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5.3-2

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For the given polynomials, list the degree of each term. Then find the degree of the entire polynomial. a. 11a5b – 5a4b3 + 6b b. 8m2n2 + mn5 – 9 c. –7
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5.3-3

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Classify each of the following as linear equation in one variable, linear equation in two variables, linear expression in one or more variables, or not linear. Explain each classification. a. y = 0.2x b. 3x – 7y + 2
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5.3-4ab

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Classify each of the following as linear equation in one variable, linear equation in two variables, linear expression in one or more variables, or not linear. Explain each classification. c. y = 5x2 – 4x + 10 d. 4x – 3
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5.3-4cd

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Classify each of the following as linear equation in one variable, linear equation in two variables, linear expression in one or more variables, or not linear. Explain each classification. e. 4xy = 6
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5.3-4e

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Add the following polynomials. a. (8a2 + 4a + 5) + (2a2 + 3a + 7) b. (10m2 – 5mn – 6n2) + (3m2 – 3mn + 2n2) c. Find the sum of 7x and 12x2 – 8x + 5.
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5.3-5

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Subtract the following polynomials. a. (6x2 + 3x + 9) – (4x2 + x – 2) b. (8a2 – 7a – 9) – (12a2 + 4a – 12) c. Subtract –5m2 – 8m + 15 from 3m2 + 7m.
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5.3-6

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The cost in dollars to assemble b bikes can be estimated by using the polynomial 25b The cost in dollars for the parts for b bikes can be estimated by using the polynomial 65b a. Find a new polynomial that gives the total cost for the parts and assembly of b bikes.
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5.3-7a

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The cost in dollars to assemble b bikes can be estimated by using the polynomial 25b The cost in dollars for the parts for b bikes can be estimated by using the polynomial 65b b. Use your new polynomial to find the total cost for parts and assembly of 20 bikes.
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5.3-7b

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Write a polynomial that represents the total measurement of the two angles.
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5.3-8

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Find each product. a. 5(2x2 + 4x – 9) b. 7m(6m + 3) c. 2a(8a2 – 6a + 7)
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5.4-1

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Find each product, and simplify. a. (3a – 4)(5a2 + 2a – 8) b. (x2y + 7xy)(4x5 + 2y – 4)
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5.4-2

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Find each product. a. 3x(4x + 5)(2x – 3) b. –6m(4m + n)(3m – 5n)
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5.4-3

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Find each product. a. (a + 2)(a + 7) b. (2x – 5)(3x + 2) c. (7m + 4n)(m – 2n)
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5.4-4

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The wholesale cost in dollars of c cases of local oranges can be estimated by using the expression 8c After a large winter storm, the price doubled. Write an expression for the wholesale cost of local oranges after the storm.
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5.4-5

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The average amount of milk consumed per person in the United States t years since 2000 can be estimated by using the expression –0.3t gallons per person. The population of the United States in millions can be estimated by using the expression 2.75t million people. a. Write a new expression to represent the total amount of milk consumed by the U.S. population.
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5.4-6a

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The average amount of milk consumed per person in the United States t years since 2000 can be estimated by using the expression –0.3t gallons per person. The population of the United States in millions can be estimated by using the expression 2.75t million people. b. Use the expression found in part a to estimate the amount of milk that will be consumed by the U.S. population in 2015.
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5.4-6b

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Write a polynomial that represents the area of the following rectangle.
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5.4-7

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Find each product. a. (x + 4)2 b. (3x – 7)2
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5.4-8ab

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Find each product. c. d.
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5.4-8cd

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Identify the expression inside the parentheses as a product or a sum. Then multiply each expression. Simplify. a. (7x)2 b. (7 + x)2
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5.4-9

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Find each product. a. (a + 6)(a – 6) b. (2x – 5)(2x + 5) c. (3p5 + 7)(3p5 – 7)
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5.4-10

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Perform the indicated operations, and simplify. a. 8x2 – 9 + (x – 6)(5x + 2) b. (x – 7)2 – (x + 9)2
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5.4-11

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Divide and simplify. a. b.
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5.5-1

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Divide and simplify. a. b.
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5.5-2

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Divide. a. (x2 + 8x + 15) ÷ (x + 3) b. (8x2 + 2x – 21) ÷ (2x – 3)
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5.5-3

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Find an expression that represents the length of the missing side of this rectangle.
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5.5-4

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Divide, and check the result. a. (10x2 – 27x + 30) ÷ (2x – 3)
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5.5-5a

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Divide, and check the result. b. (10x3 + 63x2 + 71x – 79) ÷ (x + 3)
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5.5-5b

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Divide, and check the result. a. (4x3 – x2) ÷ (x + 5)
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5.5-6a

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Divide, and check the result. b. (27x3 – 8) ÷ (3x – 2)
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5.5-6b