College Algebra 6/e   Barnett/Ziegler/Byleen
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Chapter 1: Basic Algebraic Operations

Worked Exercises

Chapter 1: Basic Algebraic Operations

Write the set using the listing method; that is, list the elements between braces. If the set is empty, write .


Solution

The statement illustrates the use of one of the following properties or definitions. Indicate which one.
Commutative (+, ·)
Associative (+, ·)
Distributive
Identity (+, ·)
Inverse (+, ·)
Subtraction
Division
Negatives (Theorem 1)
Zero (Theorem 2)


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Indicate which of the following are true:


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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:


Solution

If A = {1, 2, 3, 4} and B = {2, 4, 6}, find:


Solution

Perform the indicated operations and simplify.


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The following expressions are calculus-related. Perform the indicated operations and simplify.


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APPLICATION


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Factor completely relative to integers.


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Factor completely relative to the integers. If a polynomial is prime relative to the integers, say so.


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The expression is calculus-related. Factor it completely relative to the integers.


Solution

Factor completely relative to the integers. In polynomials involving more than three terms, try grouping the terms in various combinations as a first step. If a polynomial is prime relative to the integers, say so.


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APPLICATION


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Perform the indicated operations and reduce your answers to lowest terms. Represent any compound fractions as simple fractions reduced to lowest terms.


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The expression is calculus-related. Reduce the fraction to lowest terms.


Solution

Perform the indicated operations and reduce answers to lowest terms. Represent any compound fractions as simple fractions reduced to lowest terms.


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Simplify the expression and write your answer using positive exponents only. Write compound fractions as simple fractions.


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Evaluate the expression to three significant digits using scientific notation if appropriate and a calculator.


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Evaluate the expression if it results in a rational number.


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Simplify the expression and express the answer using positive exponents only.


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In the following expression, m and n represent positive integers. Simplify it and express answers using positive exponents.


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APPLICATIONS


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Change to radical form. Do not simplify.


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Change to rational exponent form. Do not simplify.


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Write in simplified form.


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Rationalize the denominator and write in simplified form.


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Write in simplified form.


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Rationalize the denominator and write in simplified form.


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For what real number is the expression true?


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