College Algebra
10th Edition
ISBN: 9781337282291
Author: Ron Larson
Publisher: Cengage Learning
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Textbook Question
Chapter P.2, Problem 24E
Using Properties of Exponents In Exercises 21-26, simplify each expression.
(a)
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Chapter P Solutions
College Algebra
Ch. P.1 - Repeat Example 1 for the set...Ch. P.1 - Plot the real numbers on the real number line....Ch. P.1 - Place the appropriate inequality symbol or between...Ch. P.1 - Describe the subset of real numbers that the...Ch. P.1 - Give a verbal description of the interval 2,5.Ch. P.1 - Prob. 6ECPCh. P.1 - Evaluate each expression. a. 1 b. 34 c. 23 d. 0.7Ch. P.1 - Evaluate x+3x+3 for (a) x3 and (b) x3 .Ch. P.1 - Place the appropriate symbol ,,or= between the...Ch. P.1 - a. Find the distance between 35 and 23 . b. Find...
Ch. P.1 - Identify the terms and coefficients of 2x+4 .Ch. P.1 - Evaluate 4x5 when x=0 .Ch. P.1 - Identify the rule of algebra illustrated by the...Ch. P.1 - a. Multiply fractions: 35x6 b. Add fractions: .Ch. P.1 - Prob. 1ECh. P.1 - Prob. 2ECh. P.1 - Prob. 3ECh. P.1 - Prob. 4ECh. P.1 - Prob. 5ECh. P.1 - Prob. 6ECh. P.1 - Classifying Real Numbers In Exercises 7-10,...Ch. P.1 - Prob. 8ECh. P.1 - Prob. 9ECh. P.1 - Prob. 10ECh. P.1 - Prob. 11ECh. P.1 - Plotting Points on the Real Number Line In...Ch. P.1 - Plotting and Ordering Real Numbers In Exercises...Ch. P.1 - Prob. 14ECh. P.1 - Prob. 15ECh. P.1 - Prob. 16ECh. P.1 - Prob. 17ECh. P.1 - Interpreting an Inequality or an Interval In...Ch. P.1 - Interpreting an Inequality or an Interval In...Ch. P.1 - Interpreting an Inequality or an Interval In...Ch. P.1 - Interpreting an Inequality or an Interval In...Ch. P.1 - Interpreting an Inequality or an Interval In...Ch. P.1 - Interpreting an Inequality or an Interval In...Ch. P.1 - Interpreting an Inequality or an Interval In...Ch. P.1 - Using Inequality and Interval Notation In...Ch. P.1 - Prob. 26ECh. P.1 - Using Inequality and Interval Notation In...Ch. P.1 - Using Inequality and Interval Notation In...Ch. P.1 - Prob. 29ECh. P.1 - Evaluating an Absolute Value Expression In...Ch. P.1 - Prob. 31ECh. P.1 - Prob. 32ECh. P.1 - Evaluating an Absolute Value Expression In...Ch. P.1 - Prob. 34ECh. P.1 - Evaluating an Absolute Value Expression In...Ch. P.1 - Evaluating an Absolute Value Expression In...Ch. P.1 - Prob. 37ECh. P.1 - Evaluating an Absolute Value Expression In...Ch. P.1 - Prob. 39ECh. P.1 - Prob. 40ECh. P.1 - Prob. 41ECh. P.1 - Prob. 42ECh. P.1 - Finding a Distance In Exercises 43-46, find the...Ch. P.1 - Finding a Distance In Exercises 43-46, find the...Ch. P.1 - Prob. 45ECh. P.1 - Prob. 46ECh. P.1 - Prob. 47ECh. P.1 - Prob. 48ECh. P.1 - In Exercises 49-52, use the bar graph, which shows...Ch. P.1 - In Exercises 49-52, use the bar graph, which shows...Ch. P.1 - In Exercises 49-52, use the bar graph, which shows...Ch. P.1 - In Exercises 49-52, use the bar graph, which shows...Ch. P.1 - Identifying Terms and Coefficients In Exercises...Ch. P.1 - Identifying Terms and Coefficients In Exercises...Ch. P.1 - Prob. 55ECh. P.1 - Prob. 56ECh. P.1 - Prob. 57ECh. P.1 - Identifying Terms and Coefficients In Exercises...Ch. P.1 - Prob. 59ECh. P.1 - Prob. 60ECh. P.1 - Prob. 61ECh. P.1 - Prob. 62ECh. P.1 - Prob. 63ECh. P.1 - Evaluating an Algebraic Expression In Exercises...Ch. P.1 - Prob. 65ECh. P.1 - Prob. 66ECh. P.1 - Prob. 67ECh. P.1 - Identifying Rules of Algebra In Exercises 65-68,...Ch. P.1 - Prob. 69ECh. P.1 - Operations with Fractions In Exercises 69-72,...Ch. P.1 - Prob. 71ECh. P.1 - Operations with Fractions In Exercises 69-72,...Ch. P.1 - Prob. 73ECh. P.1 - Prob. 74ECh. P.1 - True or False? In Exercises 73 -75, determine...Ch. P.1 - HOW DO YOU SEE IT? Match each description with its...Ch. P.1 - Prob. 77ECh. P.2 - Evaluate each expression. a. 34 b. 34 c. 323 d....Ch. P.2 - Evaluate each algebraic expression when x=4 . a....Ch. P.2 - Use the properties of exponents to simplify each...Ch. P.2 - Prob. 4ECPCh. P.2 - Write 45,850 in scientific notation.Ch. P.2 - Prob. 6ECPCh. P.2 - Evaluate 24,000,000,0000.00000012300,000 .Ch. P.2 - Prob. 8ECPCh. P.2 - Prob. 9ECPCh. P.2 - Simplify each radical expression. a. 32 b. 2503 c....Ch. P.2 - Prob. 11ECPCh. P.2 - Rationalize the denominator of each expression. a....Ch. P.2 - Rationalize the denominator: 862 .Ch. P.2 - Rationalize the numerator: 223Ch. P.2 - Write (a) 273 , (b) x3y5z, and (c) 3x3x2 in...Ch. P.2 - Write each expression in radical form. a. x271/2...Ch. P.2 - Prob. 17ECPCh. P.2 - Fill in the blanks. In the exponential form an, n...Ch. P.2 - Prob. 2ECh. P.2 - Prob. 3ECh. P.2 - Prob. 4ECh. P.2 - Fill in the blanks. Radical expressions can be...Ch. P.2 - Fill in the blanks. The expressions a+bm and abm...Ch. P.2 - Prob. 7ECh. P.2 - Prob. 8ECh. P.2 - Prob. 9ECh. P.2 - Prob. 10ECh. P.2 - Evaluating Exponential Expressions In Exercises...Ch. P.2 - Prob. 12ECh. P.2 - Prob. 13ECh. P.2 - Prob. 14ECh. P.2 - Evaluating an Algebraic Expression In Exercises...Ch. P.2 - Evaluating an Algebraic Expression In Exercises...Ch. P.2 - Evaluating an Algebraic Expression In Exercises...Ch. P.2 - Evaluating an Algebraic Expression In Exercises...Ch. P.2 - Evaluating an Algebraic Expression In Exercises...Ch. P.2 - Evaluating an Algebraic Expression In Exercises...Ch. P.2 - Using Properties of Exponents In Exercises 21-26,...Ch. P.2 - Using Properties of Exponents In Exercises 21-26,...Ch. P.2 - Using Properties of Exponents In Exercises 21-26,...Ch. P.2 - Using Properties of Exponents In Exercises 21-26,...Ch. P.2 - Using Properties of Exponents In Exercises 21-26,...Ch. P.2 - Using Properties of Exponents In Exercises 21-26,...Ch. P.2 - Rewriting with Positive Exponents In Exercises...Ch. P.2 - Rewriting with Positive Exponents In Exercises...Ch. P.2 - Rewriting with Positive Exponents In Exercises...Ch. P.2 - Rewriting with Positive Exponents In Exercises...Ch. P.2 - Prob. 31ECh. P.2 - Prob. 32ECh. P.2 - Prob. 33ECh. P.2 - Prob. 34ECh. P.2 - Prob. 35ECh. P.2 - Prob. 36ECh. P.2 - Prob. 37ECh. P.2 - Prob. 38ECh. P.2 - Prob. 39ECh. P.2 - Prob. 40ECh. P.2 - Prob. 41ECh. P.2 - Prob. 42ECh. P.2 - Prob. 43ECh. P.2 - Prob. 44ECh. P.2 - Prob. 45ECh. P.2 - Prob. 46ECh. P.2 - Prob. 47ECh. P.2 - Prob. 48ECh. P.2 - Prob. 49ECh. P.2 - Prob. 50ECh. P.2 - Rationalizing a Denominator In Exercises 51-54,...Ch. P.2 - Rationalizing a Denominator In Exercises 51-54,...Ch. P.2 - Rationalizing a Denominator In Exercises 51-54,...Ch. P.2 - Prob. 54ECh. P.2 - Prob. 55ECh. P.2 - Prob. 56ECh. P.2 - Prob. 57ECh. P.2 - Prob. 58ECh. P.2 - Prob. 59ECh. P.2 - Prob. 60ECh. P.2 - Prob. 61ECh. P.2 - Simplifying Expressions In Exercises 61-68,...Ch. P.2 - Prob. 63ECh. P.2 - Prob. 64ECh. P.2 - Prob. 65ECh. P.2 - Prob. 66ECh. P.2 - Prob. 67ECh. P.2 - Prob. 68ECh. P.2 - Mathematical Modeling A funnel is filled with...Ch. P.2 - HOW DO YOU SEE IT? Package A is a cube with a...Ch. P.2 - Prob. 71ECh. P.2 - Prob. 72ECh. P.2 - Prob. 73ECh. P.2 - Prob. 74ECh. P.3 - Write the polynomial 67x3+2x in standard form....Ch. P.3 - Find the difference2x3x+3x22x3 and write the...Ch. P.3 - Prob. 3ECPCh. P.3 - Multiply x2+2x+3 by x22x+3 using a vertical...Ch. P.3 - Prob. 5ECPCh. P.3 - Prob. 6ECPCh. P.3 - Find 4x13.Ch. P.3 - Find the product of x2+3y and x23y.Ch. P.3 - Prob. 9ECPCh. P.3 - Prob. 1ECh. P.3 - Prob. 2ECh. P.3 - Prob. 3ECh. P.3 - Prob. 4ECh. P.3 - Prob. 5ECh. P.3 - Prob. 6ECh. P.3 - Writing Polynomials in Standard Form In Exercises...Ch. P.3 - Prob. 8ECh. P.3 - Prob. 9ECh. P.3 - Prob. 10ECh. P.3 - Prob. 11ECh. P.3 - Prob. 12ECh. P.3 - Prob. 13ECh. P.3 - Prob. 14ECh. P.3 - Prob. 15ECh. P.3 - Prob. 16ECh. P.3 - Adding or Subtracting Polynomials In Exercises...Ch. P.3 - Prob. 18ECh. P.3 - Prob. 19ECh. P.3 - Adding or Subtracting Polynomials In Exercises...Ch. P.3 - Prob. 21ECh. P.3 - Prob. 22ECh. P.3 - Prob. 23ECh. P.3 - Prob. 24ECh. P.3 - Prob. 25ECh. P.3 - Prob. 26ECh. P.3 - Multiplying Polynomials In Exercises 25-38,...Ch. P.3 - Prob. 28ECh. P.3 - Prob. 29ECh. P.3 - Prob. 30ECh. P.3 - Multiplying Polynomials In Exercises 25-38,...Ch. P.3 - Prob. 32ECh. P.3 - Prob. 33ECh. P.3 - Prob. 34ECh. P.3 - Prob. 35ECh. P.3 - Prob. 36ECh. P.3 - Prob. 37ECh. P.3 - Prob. 38ECh. P.3 - Prob. 39ECh. P.3 - Prob. 40ECh. P.3 - Prob. 41ECh. P.3 - Prob. 42ECh. P.3 - Finding Special Products In Exercises 39-62, find...Ch. P.3 - Prob. 44ECh. P.3 - Prob. 45ECh. P.3 - Prob. 46ECh. P.3 - Prob. 47ECh. P.3 - Prob. 48ECh. P.3 - Prob. 49ECh. P.3 - Prob. 50ECh. P.3 - Prob. 51ECh. P.3 - Prob. 52ECh. P.3 - Prob. 53ECh. P.3 - Prob. 54ECh. P.3 - Prob. 55ECh. P.3 - Prob. 56ECh. P.3 - Prob. 57ECh. P.3 - Prob. 58ECh. P.3 - Prob. 59ECh. P.3 - Prob. 60ECh. P.3 - Prob. 61ECh. P.3 - Prob. 62ECh. P.3 - Prob. 63ECh. P.3 - Prob. 64ECh. P.3 - Prob. 65ECh. P.3 - Prob. 66ECh. P.3 - Prob. 67ECh. P.3 - Prob. 68ECh. P.3 - Prob. 69ECh. P.3 - Prob. 70ECh. P.3 - Prob. 71ECh. P.3 - Prob. 72ECh. P.3 - Genetics In deer, the gene N is for normal...Ch. P.3 - Construction Management A square-shaped foundation...Ch. P.3 - Geometry In Exercises 75-78, find the area of the...Ch. P.3 - Geometry In Exercises 75-78, find the area of the...Ch. P.3 - Geometry In Exercises 75-78, find the area of the...Ch. P.3 - Geometry In Exercises 75-78, find the area of the...Ch. P.3 - Volume of a Box A take-out fast-food restaurant is...Ch. P.3 - Volume of a Box An overnight shipping company...Ch. P.3 - Prob. 81ECh. P.3 - Stopping distance, The stopping distance of an...Ch. P.3 - Prob. 83ECh. P.3 - Prob. 84ECh. P.3 - Prob. 85ECh. P.3 - Prob. 86ECh. P.3 - Prob. 87ECh. P.3 - Degree of a Sum Find the degree of the sum of two...Ch. P.3 - Prob. 89ECh. P.3 - Prob. 90ECh. P.3 - Prob. 91ECh. P.3 - Prob. 92ECh. P.4 - Factor each expression. a. 5x315x2 b. 3+6x12x3 c....Ch. P.4 - Prob. 2ECPCh. P.4 - Prob. 3ECPCh. P.4 - Prob. 4ECPCh. P.4 - Prob. 5ECPCh. P.4 - Factor each expression. a. x3+216 b. 5y3+135Ch. P.4 - Prob. 7ECPCh. P.4 - Prob. 8ECPCh. P.4 - Prob. 9ECPCh. P.4 - Prob. 10ECPCh. P.4 - Prob. 1ECh. P.4 - Prob. 2ECh. P.4 - Prob. 3ECh. P.4 - Prob. 4ECh. P.4 - Factoring Out a Common Factor In Exercises 5-8,...Ch. P.4 - Factoring Out a Common Factor In Exercises 5-8,...Ch. P.4 - Prob. 7ECh. P.4 - Prob. 8ECh. P.4 - Factoring the Difference of Two Squares In...Ch. P.4 - Prob. 10ECh. P.4 - Prob. 11ECh. P.4 - Factoring the Difference of Two Squares In...Ch. P.4 - Prob. 13ECh. P.4 - Prob. 14ECh. P.4 - Factoring the Difference of Two Squares In...Ch. P.4 - Prob. 16ECh. P.4 - Prob. 17ECh. P.4 - Factoring the Difference of Two Squares In...Ch. P.4 - Prob. 19ECh. P.4 - Prob. 20ECh. P.4 - Factoring a Perfect Square Trinomial In Exercises...Ch. P.4 - Prob. 22ECh. P.4 - Prob. 23ECh. P.4 - Factoring a Perfect Square Trinomial In Exercises...Ch. P.4 - Factoring the Sum or Difference of Two Cubes In...Ch. P.4 - Prob. 26ECh. P.4 - Factoring the Sum or Difference of Two Cubes In...Ch. P.4 - Prob. 28ECh. P.4 - Prob. 29ECh. P.4 - Factoring the Sum or Difference of Two Cubes In...Ch. P.4 - Prob. 31ECh. P.4 - Prob. 32ECh. P.4 - Factoring a Trinomial In Exercises 33-42, factor...Ch. P.4 - Prob. 34ECh. P.4 - Prob. 35ECh. P.4 - Factoring a Trinomial In Exercises 33-42, factor...Ch. P.4 - Prob. 37ECh. P.4 - Prob. 38ECh. P.4 - Factoring a Trinomial In Exercises 33-42, factor...Ch. P.4 - Prob. 40ECh. P.4 - Prob. 41ECh. P.4 - Factoring a Trinomial In Exercises 33-42, factor...Ch. P.4 - Prob. 43ECh. P.4 - Prob. 44ECh. P.4 - Factoring by Grouping In Exercises 43-48, factor...Ch. P.4 - Prob. 46ECh. P.4 - Prob. 47ECh. P.4 - Factoring by Grouping In Exercises 43-48, factor...Ch. P.4 - Prob. 49ECh. P.4 - Prob. 50ECh. P.4 - Factoring a Trinomial by Grouping In Exercises...Ch. P.4 - Prob. 52ECh. P.4 - Prob. 53ECh. P.4 - Factoring Completely In Exercises 53-70,...Ch. P.4 - Prob. 55ECh. P.4 - Prob. 56ECh. P.4 - Factoring Completely In Exercises 53-70,...Ch. P.4 - Prob. 58ECh. P.4 - Prob. 59ECh. P.4 - Factoring Completely In Exercises 53-70,...Ch. P.4 - Prob. 61ECh. P.4 - Prob. 62ECh. P.4 - Prob. 63ECh. P.4 - Prob. 64ECh. P.4 - Prob. 65ECh. P.4 - Prob. 66ECh. P.4 - Prob. 67ECh. P.4 - Prob. 68ECh. P.4 - Prob. 69ECh. P.4 - Prob. 70ECh. P.4 - Prob. 71ECh. P.4 - Prob. 72ECh. P.4 - Prob. 73ECh. P.4 - Prob. 74ECh. P.4 - Prob. 75ECh. P.4 - Prob. 76ECh. P.4 - Geometric Modeling In Exercises 77-80, draw a...Ch. P.4 - Geometric Modeling In Exercises 77-80, draw a...Ch. P.4 - Prob. 79ECh. P.4 - Prob. 80ECh. P.4 - Geometry In Exercises 81 and 82, write an...Ch. P.4 - Prob. 82ECh. P.4 - Geometry The cylindrical shell shown in the figure...Ch. P.4 - The rate of change of an autocatalytic chemical...Ch. P.4 - Prob. 85ECh. P.4 - Prob. 86ECh. P.4 - Prob. 87ECh. P.4 - Prob. 88ECh. P.4 - True or False? In Exercises 89 and 90, determine...Ch. P.4 - Prob. 90ECh. P.4 - Error Analysis Describe the error....Ch. P.4 - Prob. 92ECh. P.4 - Prob. 93ECh. P.4 - Prob. 94ECh. P.4 - Prob. 95ECh. P.4 - HOW DO YOU SEE IT? The figure shows a large square...Ch. P.4 - Prob. 97ECh. P.5 - Find the domain of each expression. a. 4x3+3,x0 b....Ch. P.5 - Write 4x+12x23x18 in simplest form.Ch. P.5 - Prob. 3ECPCh. P.5 - Prob. 4ECPCh. P.5 - Prob. 5ECPCh. P.5 - Prob. 6ECPCh. P.5 - Prob. 7ECPCh. P.5 - Prob. 8ECPCh. P.5 - Prob. 9ECPCh. P.5 - Prob. 10ECPCh. P.5 - Prob. 11ECPCh. P.5 - Prob. 1ECh. P.5 - Prob. 2ECh. P.5 - Prob. 3ECh. P.5 - Prob. 4ECh. P.5 - Prob. 5ECh. P.5 - Prob. 6ECh. P.5 - Prob. 7ECh. P.5 - Prob. 8ECh. P.5 - Prob. 9ECh. P.5 - Prob. 10ECh. P.5 - Prob. 11ECh. P.5 - Finding the Domain of an Algebraic Expression In...Ch. P.5 - Finding the Domain of an Algebraic Expression In...Ch. P.5 - Finding the Domain of an Algebraic Expression In...Ch. P.5 - Prob. 15ECh. P.5 - Prob. 16ECh. P.5 - Prob. 17ECh. P.5 - Prob. 18ECh. P.5 - Prob. 19ECh. P.5 - Prob. 20ECh. P.5 - Prob. 21ECh. P.5 - Prob. 22ECh. P.5 - Simplifying a Rational Expression In Exercises...Ch. P.5 - Prob. 24ECh. P.5 - Prob. 25ECh. P.5 - Prob. 26ECh. P.5 - Prob. 27ECh. P.5 - Prob. 28ECh. P.5 - Prob. 29ECh. P.5 - Prob. 30ECh. P.5 - Prob. 31ECh. P.5 - Evaluating a Rational Expression Complete the...Ch. P.5 - Prob. 33ECh. P.5 - Prob. 34ECh. P.5 - Prob. 35ECh. P.5 - Prob. 36ECh. P.5 - Prob. 37ECh. P.5 - Prob. 38ECh. P.5 - Prob. 39ECh. P.5 - Prob. 40ECh. P.5 - Prob. 41ECh. P.5 - Prob. 42ECh. P.5 - Adding or Subtracting Rational Expressions In...Ch. P.5 - Prob. 44ECh. P.5 - Prob. 45ECh. P.5 - Prob. 46ECh. P.5 - Prob. 47ECh. P.5 - Prob. 48ECh. P.5 - Prob. 49ECh. P.5 - Prob. 50ECh. P.5 - Prob. 51ECh. P.5 - Prob. 52ECh. P.5 - Prob. 53ECh. P.5 - Prob. 54ECh. P.5 - Prob. 55ECh. P.5 - Prob. 56ECh. P.5 - Prob. 57ECh. P.5 - Prob. 58ECh. P.5 - Prob. 59ECh. P.5 - Prob. 60ECh. P.5 - Prob. 61ECh. P.5 - Prob. 62ECh. P.5 - Prob. 63ECh. P.5 - Prob. 64ECh. P.5 - Prob. 65ECh. P.5 - Prob. 66ECh. P.5 - Prob. 67ECh. P.5 - Rewriting a Difference Quotient In Exercises...Ch. P.5 - Prob. 69ECh. P.5 - Prob. 70ECh. P.5 - Prob. 71ECh. P.5 - Prob. 72ECh. P.5 - Probability In Exercises 73 and 74, consider an...Ch. P.5 - Probability In Exercises 73 and 74, consider an...Ch. P.5 - Prob. 75ECh. P.5 - Finance The formula that approximates the annual...Ch. P.5 - Prob. 77ECh. P.5 - Prob. 78ECh. P.5 - Prob. 79ECh. P.5 - Prob. 80ECh. P.6 - Plot the points 3,2,4,2,3,1,0,2, and 1,2.Ch. P.6 - Prob. 2ECPCh. P.6 - Prob. 3ECPCh. P.6 - Prob. 4ECPCh. P.6 - Find the midpoint of the line segment joining the...Ch. P.6 - A football quarterback throws a pass from the...Ch. P.6 - Prob. 7ECPCh. P.6 - Prob. 8ECPCh. P.6 - Prob. 1ECh. P.6 - Prob. 2ECh. P.6 - Prob. 3ECh. P.6 - Fill in the blanks. Finding the average values of...Ch. P.6 - Plotting Points in the Cartesian Plane In...Ch. P.6 - Prob. 6ECh. P.6 - Prob. 7ECh. P.6 - Prob. 8ECh. P.6 - Prob. 9ECh. P.6 - Determining Quadrant(s) for a Point In Exercises...Ch. P.6 - Prob. 11ECh. P.6 - Prob. 12ECh. P.6 - Prob. 13ECh. P.6 - Prob. 14ECh. P.6 - Prob. 15ECh. P.6 - Sketching a Scatter Plot In Exercises 15 and 16,...Ch. P.6 - Prob. 17ECh. P.6 - Prob. 18ECh. P.6 - Prob. 19ECh. P.6 - Prob. 20ECh. P.6 - Prob. 21ECh. P.6 - Prob. 22ECh. P.6 - Verifying a Right Triangle In Exercises 23 and 24,...Ch. P.6 - Prob. 24ECh. P.6 - Prob. 25ECh. P.6 - Verifying a Polygon In Exercises 25-28, show that...Ch. P.6 - Verifying a Polygon In Exercises 25-28, show that...Ch. P.6 - Prob. 28ECh. P.6 - Prob. 29ECh. P.6 - Prob. 30ECh. P.6 - Prob. 31ECh. P.6 - Prob. 32ECh. P.6 - Prob. 33ECh. P.6 - Prob. 34ECh. P.6 - Prob. 35ECh. P.6 - Plotting, Distance, and Midpoint In Exercises...Ch. P.6 - An airplane flies from Naples, Italy, in a...Ch. P.6 - Sports A soccer player passes the ball from a...Ch. P.6 - Prob. 39ECh. P.6 - Prob. 40ECh. P.6 - Translating Points in the Plane In Exercises...Ch. P.6 - Prob. 42ECh. P.6 - Prob. 43ECh. P.6 - Translating Points in the Plane In Exercises...Ch. P.6 - Minimum Wage Use the graph below, which shows the...Ch. P.6 - Exam Scores The table shows the mathematics...Ch. P.6 - Prob. 47ECh. P.6 - Prob. 48ECh. P.6 - True or False? In Exercises 47-50, determine...Ch. P.6 - Prob. 50ECh. P.6 - Think About It When plotting points on the...Ch. P.6 - Think About It What is the ycoordinate of any...Ch. P.6 - Prob. 53ECh. P.6 - Using the Midpoint Formula Use the result of...Ch. P.6 - Prob. 55ECh. P.6 - Prob. 56ECh. P.6 - Proof Prove that the diagonals of the...Ch. P.6 - HOW DO YOU SEE IT? Use the plot of the point x0,y0...Ch. P.6 - Collinear Points Three or more points are...Ch. P.6 - Prob. 60ECh. P - Prob. 1RECh. P - Prob. 2RECh. P - Plotting and Ordering Real Numbers In Exercises 3...Ch. P - Prob. 4RECh. P - Interpreting an Inequality or an Interval In...Ch. P - Prob. 6RECh. P - Interpreting an Inequality or an Interval In...Ch. P - Prob. 8RECh. P - Prob. 9RECh. P - Prob. 10RECh. P - Prob. 11RECh. P - Prob. 12RECh. P - Prob. 13RECh. P - Prob. 14RECh. P - Prob. 15RECh. P - Prob. 16RECh. P - Prob. 17RECh. P - Prob. 18RECh. P - Prob. 19RECh. P - Prob. 20RECh. P - Prob. 21RECh. P - Prob. 22RECh. P - Prob. 23RECh. P - Prob. 24RECh. P - Prob. 25RECh. P - Prob. 26RECh. P - Prob. 27RECh. P - Prob. 28RECh. P - Prob. 29RECh. P - Prob. 30RECh. P - Prob. 31RECh. P - Prob. 32RECh. P - Prob. 33RECh. P - Prob. 34RECh. P - Prob. 35RECh. P - Prob. 36RECh. P - Prob. 37RECh. P - Prob. 38RECh. P - Prob. 39RECh. P - Prob. 40RECh. P - Prob. 41RECh. P - Prob. 42RECh. P - Prob. 43RECh. P - Prob. 44RECh. P - Prob. 45RECh. P - Prob. 46RECh. P - Prob. 47RECh. P - Prob. 48RECh. P - Prob. 49RECh. P - Prob. 50RECh. P - Prob. 51RECh. P - Prob. 52RECh. P - Prob. 53RECh. P - Prob. 54RECh. P - Prob. 55RECh. P - Prob. 56RECh. P - Prob. 57RECh. P - Prob. 58RECh. P - Prob. 59RECh. P - Prob. 60RECh. P - Prob. 61RECh. P - Prob. 62RECh. P - Prob. 63RECh. P - Prob. 64RECh. P - Prob. 65RECh. P - Prob. 66RECh. P - Prob. 67RECh. P - Prob. 68RECh. P - Prob. 69RECh. P - Prob. 70RECh. P - Prob. 71RECh. P - Prob. 72RECh. P - Prob. 73RECh. P - Prob. 74RECh. P - Prob. 75RECh. P - Prob. 76RECh. P - Prob. 77RECh. P - Prob. 78RECh. P - Geometry Find a polynomial that represents the...Ch. P - Geometry Use the area model to write two different...Ch. P - Prob. 81RECh. P - Prob. 82RECh. P - Prob. 83RECh. P - Prob. 84RECh. P - Prob. 85RECh. P - Prob. 86RECh. P - Prob. 87RECh. P - Prob. 88RECh. P - Prob. 89RECh. P - Factoring Completely In Exercises 81-90,...Ch. P - Prob. 91RECh. P - Prob. 92RECh. P - Prob. 93RECh. P - Prob. 94RECh. P - Prob. 95RECh. P - Prob. 96RECh. P - Prob. 97RECh. 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- Rewriting with Positive Exponents In Exercises 27-30, rewrite each expression with positive exponents. Simplify, if possible. (a) 4y28y4 (b) z+23z+21arrow_forwardEvaluating an Algebraic Expression In Exercises 15-20, evaluate the expression for the given value of x. 7x2,x=4arrow_forwardEXAMPI E 7 Simplify each expression. Assume that all variables represent positive real numbers. Write all answers using positive exponents only. a8/3a1/3 a? (a) 52/753/7 (b) (52/7)3 (c) (a2/363/2,6 (d) Strategy We will use the product, power, and quotient rules for exponents to simplify each expression. Why The familiar rules for exponents are valid for rational exponents. Solution (a) 52/753/7 = 52/7 + 3/7 Use the rule xmx" = xm + n. 2 3 5 = 55/7 Add: 7 (b) (52/7)3 = 5(2/7)(3) Use the rule (xm)" = xmn. = 56/7 Multiply: 극(3)-극(클) -윽 (c) (a2/3b1/2)6 = (a2/3)6(b1/2)6 = a12/366/2 Use the rule (xy)" = x^y^. Use the rule (xm)" = xmn twice. Simplify the exponents. a8/3a1/3 a? Use the rules xmx" = xm + n ut - n (d) a8/3 + 1/3 – 2 and %3D = a8/3 + 1/3 – 6/3 2 = 3 8 3 = a3/3 1 + 3 %D 3 3 3 = 1. 3arrow_forward
- 3arrow_forwardEXAMPLE 1 Simplify each expression. Assume that x can represent any nonzero real number. (a) 64-1/2 (b) (-16)-5/4 (c) -625-3/4 (d) (-32x5)-2/5 and (e) 1 25-3/2 Strategy 1 or x-m/n We will use one of the rules x-m/n 1 xm/n to write the reciprocal of each exponential expression and change the exponent's sign to positive. tm/n Why If we can produce an equivalent expression having a positive rational exponent, we can use the methods of this section to simplify it. Solution 1 Because the exponent is negative, write the reciprocal of 64¬1/2, and change the sign of the 1 (a) 64-1/2 641/2 64 8. exponent. (b) (-16)-5/4 is not a real number because (-16)5/4 is not a real number. (c) In -625-3/4, the base is 1 1 -625- -3/4 625)3 1 1 %3D %3D %D 6253/4 53 125 1 1 (d) (-32x5)-2/5 = 1 %D %D (-32x5)2/5 ¯ (V-32x5)2 (-2x)² 1 (e) -3/2 = 253/2 = (/25)³ = 53 = Because the exponent is negative, write the reciprocal of 1 25-3/2 and change the sign of the 25-3/2' exponent. ||arrow_forward(a) Explain the meaning of the exponent in the expression 23 . (b) Explain the meaning of the exponent in the expression 23 .arrow_forward
- What are the three uses of the “-” sign in algebra? Explain how they differ.arrow_forwardDistance The distance between Earth and one of the brightest stars in the night star is 33.7 light years. One light year is about 6,000,000,000,000 (6 trillion), miles. (a) Write the number of miles in one light year in scientific notation. (b) Use scientific notation to find the distance between Earth and the star in miles. Write the answer in scientific notation.arrow_forwardThe Gross Domestic Product (GDP) for the United States in the first quarter of 2014 was 1.714961013 . Rewrite the GDP in standard notation.arrow_forward
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