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12th Edition

Ronald J. Harshbarger + 1 other

Publisher: Cengage Learning

ISBN: 9781337625340

Chapter 0.3, Problem 13E

Textbook Problem

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In problems 9-18, simplify the expressions with all exponents positive.

To determine

**To calculate:** The value of the expression

**Given information:**

The provided expression is

**Formula used:**

The following formulas are used to solve the expression:

Here, *a* and *b* are any real numbers not equal to zero, and *m* and *n* are integers.

Product rule of exponent:

Quotient rule of exponent:

Negative exponent:

Zero exponent:

**Calculation:**

Consider the expression

According to the product rule of the exponents, the expression is written as follows:

Mathematical Applications for the Management, Life, and Social Sciences

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Ch. 0.1 - CHECK POINT
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Ch. 0.2 - In Problems, indicate whether the given expression...Ch. 0.2 - In Problems, indicate whether the given expression...Ch. 0.2 - Which property of real numbers is illustrated in...Ch. 0.2 - Which property of real numbers is illustrated in...Ch. 0.2 - Which property of real numbers is illustrated in...Ch. 0.2 - Which property of real numbers is illustrated in...Ch. 0.2 - Insert the proper sign to replacein problems...Ch. 0.2 - Insert the proper sign to replacein problems...Ch. 0.2 - Insert the proper sign to replacein problems...Ch. 0.2 - Insert the proper sign to replacein problems...Ch. 0.2 - Insert the proper sign to replacein problems...Ch. 0.2 - Insert the proper sign to replacein problems...Ch. 0.2 - Insert the proper sign to replacein problems...Ch. 0.2 - Insert the proper sign to replacein problems...Ch. 0.2 - In problems 15-26,evaluate each expression.
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Ch. 0.2 - In problems 15-26, evaluate each expression.
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Ch. 0.2 - In problems 15-26, evaluate each expression.
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Ch. 0.2 - In problems 15-26, evaluate each expression.
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Ch. 0.2 - In problems 15-26, evaluate each expression.
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Ch. 0.2 - In problems 15-26, evaluate each expression.
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Ch. 0.2 - In problems 15-26, evaluate each expression.
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26.
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What part of the real number line corresponds to...Ch. 0.2 - 28. Write the interval corresponding to .
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1. Complete the following.
(a) (b) ...Ch. 0.3 - CHECK POINT
2. True or false:
(a) (b) (c)
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Compound interest if is invested ...Ch. 0.3 - APPLICATIONS
Compound interest if is invested ...Ch. 0.3 - APPLICATIONS
Compound interest if is invested ...Ch. 0.3 - APPLICATIONS
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Which of the following are not real...Ch. 0.4 - CHECK POINT
2. (a) W rite as radicals.
...Ch. 0.4 - CHECK POINT
3. Evaluate the following.
(a) (b) ...Ch. 0.4 - 4. Complete the following.
(a) (b) (c) ...Ch. 0.4 - 5. True or false.
(a) (b) (c) ...Ch. 0.4 - CHECK POINT
6. Simplify.
Ch. 0.4 - CHECK POINT
7. Rationalize the denominator of if...Ch. 0.4 - In problems 1-4, fnd the powers and roots,if they...Ch. 0.4 - In problems 1-4, fnd the powers and roots,if they...Ch. 0.4 - In problems 1-4, fnd the powers and roots,if they...Ch. 0.4 - In problems 1-4, fnd the powers and roots,if they...Ch. 0.4 - In problems 5and 6,rewrite each radical with a...Ch. 0.4 - In problems 5and 6,rewrite each radical with a...Ch. 0.4 - In problems 7-10, replace each radical with a...Ch. 0.4 - In problems 7-10, replace each radical with a...Ch. 0.4 - In problems 7-10, replace each radical with a...Ch. 0.4 - In problems 7-10, replace each radical with a...Ch. 0.4 - In problems 11-16, write in radical form.Do not...Ch. 0.4 - In problems 11-16, write in radical form.Do not...Ch. 0.4 - In problems 11-16, write in radical form.Do not...Ch. 0.4 - In problems 11-16, write in radical form.Do not...Ch. 0.4 - In problems 11-16, write in radical form.Do not...Ch. 0.4 - In problems 11-16, write in radical form.Do not...Ch. 0.4 - In problems 17-30, simplify each expression so...Ch. 0.4 - In problems 17-30, simplify each expression so...Ch. 0.4 - In problems 17-30, simplify each expression so...Ch. 0.4 - In problems 17-30, simplify each expression so...Ch. 0.4 - In problems 17-30, simplify each expression so...Ch. 0.4 - In problems 17-30, simplify each expression so...Ch. 0.4 - In problems 17-30, simplify each expression so...Ch. 0.4 - In problems 17-30, simplify each expression so...Ch. 0.4 - In problems 17-30, simplify each expression so...Ch. 0.4 - In problems 17-30, simplify each expression so...Ch. 0.4 - In problems 17-30, simplify each expression so...Ch. 0.4 - In problems 17-30, simplify each expression so...Ch. 0.4 - In problems 17-30, simplify each expression so...Ch. 0.4 - In problems 17-30, simplify each expression so...Ch. 0.4 - In problems 31-36, simplify each expression.
31.
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32.
...Ch. 0.4 - In problems 31-36, simplify each expression.
33.
...Ch. 0.4 - In problems 31-36, simplify each expression.
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...Ch. 0.4 - In problems 31-36, simplify each expression.
35. ...Ch. 0.4 - In problems 31-36, simplify each expression.
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Ch. 0.5 - Find the following products.
Ch. 0.5 - Use long division to find.
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Ch. 0.5 - 14. Evaluate when and.
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Ch. 0.6 - Consider and observe that.
Find two expressions...Ch. 0.6 - True or false:
Ch. 0.6 - In Problems 1 and 2, factor out the common...Ch. 0.6 - In Problems 1 and 2, factor out the common...Ch. 0.6 - In Problems 3-6, factor by grouping.
3.
Ch. 0.6 - In Problems 3-6, factor by grouping.
4.
Ch. 0.6 - In Problems 3-6, factor by grouping.
5.
Ch. 0.6 - In Problems 3-6, factor by grouping.
6.
Ch. 0.6 - Factor each expression in Problems 7-18 as a...Ch. 0.6 - Factor each expression in Problems 7-18 as a...Ch. 0.6 - Factor each expression in Problems 7-18 as a...Ch. 0.6 - Factor each expression in Problems 7-18 as a...Ch. 0.6 - Factor each expression in Problems 7-18 as a...Ch. 0.6 - Factor each expression in Problems 7-18 as a...Ch. 0.6 - Factor each expression in Problems 7-18 as a...Ch. 0.6 - Factor each expression in Problems 7-18 as a...Ch. 0.6 - Factor each expression in Problems 7-18 as a...Ch. 0.6 - Factor each expression in Problems 7-18 as a...Ch. 0.6 - Factor each expression in Problems 7-18 as a...Ch. 0.6 - Factor each expression in Problems 7-18 as a...Ch. 0.6 - In Problems 19-44, factor completely.
19....Ch. 0.6 - In Problems 19-44, factor completely.
20.
Ch. 0.6 - In Problems 19-44, factor completely.
21.
Ch. 0.6 - In Problems 19-44, factor completely.
22.
Ch. 0.6 - In Problems 19-44, factor completely.
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Ch. 0.6 - In Problems 19-44, factor completely.
24.
Ch. 0.6 - In Problems 19-44, factor completely.
25.
Ch. 0.6 - In Problems 19-44, factor completely.
26.
Ch. 0.6 - In Problems 19-44, factor completely.
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Ch. 0.6 - In Problems 19-44, factor completely.
28.
Ch. 0.6 - In Problems 19-44, factor completely.
29.
Ch. 0.6 - In Problems 19-44, factor completely.
30.
Ch. 0.6 - In Problems 19-44, factor completely.
31.
Ch. 0.6 - In Problems 19-44, factor completely.
32.
Ch. 0.6 - In Problems 19-44, factor completely.
33.
Ch. 0.6 - In Problems 19-44, factor completely.
34.
Ch. 0.6 - In Problems 19-44, factor completely.
35.
Ch. 0.6 - In Problems 19-44, factor completely.
36.
Ch. 0.6 - In Problems 19-44, factor completely.
37.
Ch. 0.6 - In Problems 19-44, factor completely.
38.
Ch. 0.6 - In Problems 19-44, factor completely.
39.
Ch. 0.6 - In Problems 19-44, factor completely.
40.
Ch. 0.6 - In Problems 19-44, factor completely.
41.
Ch. 0.6 - In Problems 19-44, factor completely.
42.
Ch. 0.6 - In Problems 19-44, factor completely.
43.
Ch. 0.6 - In Problems 19-44, factor completely.
44.
Ch. 0.6 - In Problems 45-48, determine the missing...Ch. 0.6 - In Problems 45-48, determine the missing...Ch. 0.6 - In Problems 45-48, determine the missing...Ch. 0.6 - In Problems 45-48, determine the missing...Ch. 0.6 - Use the following factorization formulas involving...Ch. 0.6 - Use the following factorization formulas involving...Ch. 0.6 - Use the following factorization formulas involving...Ch. 0.6 - Use the following factorization formulas involving...Ch. 0.6 - Use the following factorization formulas involving...Ch. 0.6 - Use the following factorization formulas involving...Ch. 0.6 - Use the following factorization formulas involving...Ch. 0.6 - Use the following factorization formulas involving...Ch. 0.6 - 57. Simple interest
The future value of a...Ch. 0.6 - 58. Reaction to medication
When medicine is...Ch. 0.6 - 59. Sensitivity to medication
From the formula...Ch. 0.6 - 60. Volume
Squares of side x are cut from four...Ch. 0.6 - 61. Consumer expenditure
The consumer expenditure...Ch. 0.6 - 62. Power in a circuit
Factor the following...Ch. 0.6 - 63. Revenue
Revenue R from the sale of x units...Ch. 0.6 - 64. Poiseuille’s law
The expression for the speed...Ch. 0.7 - Simplify:
Ch. 0.7 - Multiply:
Ch. 0.7 - Divide:
Ch. 0.7 - Combine the following fractions.
Ch. 0.7 - simplify
Ch. 0.7 - 6. Rationalize the denominator: .
Ch. 0.7 - In Problems 1-6 simplify each fraction.
1. ...Ch. 0.7 - In Problems 1-6 simplify each fraction.
2. ...Ch. 0.7 - In Problems 1-6 simplify each fraction.
3. ...Ch. 0.7 - In Problems 1-6 simplify each fraction.
4. ...Ch. 0.7 - In Problems 1-6 simplify each fraction.
5. ...Ch. 0.7 - In Problems 1-6 simplify each fraction.
6. ...Ch. 0.7 - In Problems 7-34, perform the indicated operations...Ch. 0.7 - In Problems 7-34, perform the indicated operations...Ch. 0.7 - In Problems 7-34, perform the indicated operations...Ch. 0.7 - In Problems 7-34, perform the indicated operations...Ch. 0.7 - In Problems 7-34, perform the indicated operations...Ch. 0.7 - In Problems 7-34, perform the indicated operations...Ch. 0.7 - In Problems 7-34, perform the indicated operations...Ch. 0.7 - In Problems 7-34, perform the indicated operations...Ch. 0.7 - In Problems 7-34, perform the indicated operations...Ch. 0.7 - In Problems 7-34, perform the indicated operations...Ch. 0.7 - In Problems 7-34, perform the indicated operations...Ch. 0.7 - In Problems 7-34, perform the indicated operations...Ch. 0.7 - In Problems 7-34, perform the indicated operations...Ch. 0.7 - In Problems 7-34, perform the indicated operations...Ch. 0.7 - In Problems 7-34, perform the indicated operations...Ch. 0.7 - In Problems 7-34, perform the indicated operations...Ch. 0.7 - In Problems 7-34, perform the indicated operations...Ch. 0.7 - In Problems 7-34, perform the indicated operations...Ch. 0.7 - In Problems 7-34, perform the indicated operations...Ch. 0.7 - In Problems 7-34, perform the indicated operations...Ch. 0.7 - In Problems 7-34, perform the indicated operations...Ch. 0.7 - In Problems 7-34, perform the indicated operations...Ch. 0.7 - In Problems 7-34, perform the indicated operations...Ch. 0.7 - In Problems 7-34, perform the indicated operations...Ch. 0.7 - In Problems 7-34, perform the indicated operations...Ch. 0.7 - In Problems 7-34, perform the indicated operations...Ch. 0.7 - In Problems 7-34, perform the indicated operations...Ch. 0.7 - In Problems 7-34, perform the indicated operations...Ch. 0.7 - In Problems 35-42, simplify each complex...Ch. 0.7 - In Problems 35-42, simplify each complex...Ch. 0.7 - In Problems 35-42, simplify each complex...Ch. 0.7 - In Problems 35-42, simplify each complex...Ch. 0.7 - In Problems 35-42, simplify each complex...Ch. 0.7 - In Problems 35-42, simplify each complex...Ch. 0.7 - In Problems 35-42, simplify each complex...Ch. 0.7 - In Problems 35-42, simplify each complex...Ch. 0.7 - In Problems 43-46, rewrite each of the following...Ch. 0.7 - In Problems 43-46, rewrite each of the following...Ch. 0.7 - In Problems 43-46, rewrite each of the following...Ch. 0.7 - In Problems 43-46, rewrite each of the following...Ch. 0.7 - In Problems 47-50, rationalize the denominator of...Ch. 0.7 - In Problems 47-50, rationalize the denominator of...Ch. 0.7 - In Problems 47-50, rationalize the denominator of...Ch. 0.7 - In Problems 47-50, rationalize the denominator of...Ch. 0.7 - In Problems 51 and 52, rationalize the numerator...Ch. 0.7 - In Problems 51 and 52, rationalize the numerator...Ch. 0.7 - APPLICATIONS
53. Time study Workers A, B, and C...Ch. 0.7 - APPLICATIONS
54. Focal length Two thin lenses with...Ch. 0.7 - APPLICATIONS
Average cost A company’s average cost...Ch. 0.7 - APPLICATIONS
Average cost A company’s average cost...Ch. 0.7 - APPLICATIONS
57. Advertising and sales Suppose...Ch. 0.7 - APPLICATIONS
58. Annuity The formula for the...Ch. 0 - Is AB if A={1,2,5,7} and...Ch. 0 - Is it true that 3{x:x3}?Ch. 0 - Are A={1,2,3,4} and B={x:x1} disjoint?Ch. 0 - In problems 4-7, use sets...Ch. 0 - In problems 4-7, use sets...Ch. 0 - In problems 4-7, use sets...Ch. 0 - In problems 4-7, use sets...Ch. 0 - State the property of the real numbers that is...Ch. 0 - Indicate whether each given expression is one or...Ch. 0 - Insert the proper sign (,=,or) to replace each ....Ch. 0 - For Problems 11-18, evaluate each expression. |...Ch. 0 - For Problems 11-18, evaluate each expression....Ch. 0 - For Problems 11-18, evaluate each expression....Ch. 0 - For Problems 11-18, evaluate each expression....Ch. 0 - For Problems 11-18, evaluate each expression. 2[...Ch. 0 - For Problems 11-18, evaluate each expression....Ch. 0 - For Problems 11-18, evaluate each expression....Ch. 0 - For Problems 11-18, evaluate each expression....Ch. 0 - Write each inequality in interval notation, name...Ch. 0 - Write an inequality that represents each of the...Ch. 0 - Evaluate the following without a calculator. (a)...Ch. 0 - Rewrite each of the following with positive...Ch. 0 - For Problems 23-28, simplify each expression so...Ch. 0 - For Problems 23-28, simplify each expression so...Ch. 0 - For Problems 23-28, simplify each expression so...Ch. 0 - For Problems 23-28, simplify each expression so...Ch. 0 - For Problems 23-28, simplify each expression so...Ch. 0 - For Problems 23-28, simplify each expression so...Ch. 0 - Find the following roots. (a) 643 (b) 4/49 (c)...Ch. 0 - Write each of the following with an exponent and...Ch. 0 - Write each of the following in radical form. (a)...Ch. 0 - Rationalize each of the following denominators and...Ch. 0 - In Problems 33-38, simplify so that only positive...Ch. 0 - In Problems 33-38, simplify so that only positive...Ch. 0 - In Problems 33-38, simplify so that only positive...Ch. 0 - In Problems 33-38, simplify so that only positive...Ch. 0 - In Problems 33-38, simplify so that only positive...Ch. 0 - In Problems 33-38, simplify so that only positive...Ch. 0 - In Problems 39-44, simplify each expression....Ch. 0 - In Problems 39-44, simplify each expression....Ch. 0 - In Problems 39-44, simplify each expression....Ch. 0 - In Problems 39-44, simplify each expression....Ch. 0 - In Problems 39-44, simplify each expression....Ch. 0 - In Problems 39-44, simplify each expression....Ch. 0 - In problems 45-62, perform the indicated...Ch. 0 - In problems 45-62, perform the indicated...Ch. 0 - In problems 45-62, perform the indicated...Ch. 0 - In problems 45-62, perform the indicated...Ch. 0 - In problems 45-62, perform the indicated...Ch. 0 - In problems 45-62, perform the indicated...Ch. 0 - In problems 45-62, perform the indicated...Ch. 0 - In problems 45-62, perform the indicated...Ch. 0 - In problems 45-62, perform the indicated...Ch. 0 - In problems 45-62, perform the indicated...Ch. 0 - In problems 45-62, perform the indicated...Ch. 0 - In problems 45-62, perform the indicated...Ch. 0 - In problems 45-62, perform the indicated...Ch. 0 - In problems 45-62, perform the indicated...Ch. 0 - In problems 45-62, perform the indicated...Ch. 0 - In problems 45-62, perform the indicated...Ch. 0 - In problems 45-62, perform the indicated...Ch. 0 - In problems 45-62, perform the indicated...Ch. 0 - In problems 63-73, factor each expression...Ch. 0 - In problems 63-73, factor each expression...Ch. 0 - In problems 63-73, factor each expression...Ch. 0 - In problems 63-73, factor each expression...Ch. 0 - In problems 63-73, factor each expression...Ch. 0 - In problems 63-73, factor each expression...Ch. 0 - In problems 63-73, factor each expression...Ch. 0 - In problems 63-73, factor each expression...Ch. 0 - In problems 63-73, factor each expression...Ch. 0 - In problems 63-73, factor each expression...Ch. 0 - In problems 63-73, factor each expression...Ch. 0 - 74. Factor as indicated:
Ch. 0 - 75. Simplify each of the following.
(a)
(b)
Ch. 0 - In Problems 76-82, perform the indicated...Ch. 0 - In Problems 76-82, perform the indicated...Ch. 0 - In Problems 76-82, perform the indicated...Ch. 0 - In Problems 76-82, perform the indicated...Ch. 0 - In Problems 76-82, perform the indicated...Ch. 0 - In Problems 76-82, perform the indicated...Ch. 0 - In Problems 76-82, perform the indicated...Ch. 0 - In Problems 83 and 84, simplify each complex...Ch. 0 - In Problems 83 and 84, simplify each complex...Ch. 0 - Rationalize the denominator of 3x3x1 and simplify.Ch. 0 - Rationalize the denominator of xx42 and simplify.Ch. 0 - Job effectiveness factors In an attempt to...Ch. 0 - Malelabor force Using data from 1950 and projected...Ch. 0 - Poiseuilles law The expression for the speed of...Ch. 0 - Future value If an individual makes monthly...Ch. 0 - Health insurance cost The per capita net cost C...Ch. 0 - Severe weather ice makers Thunderstorms severe...Ch. 0 - Loan payment Suppose you borrow 10,000 for n...Ch. 0 - Environment Suppose that in a study of water...Ch. 0 - 95. Profit Suppose that the total cost of...Ch. 0 - 96. Business loss Suppose that a commercial...Ch. 0 - Revenue The revenue for a boat tour is...Ch. 0 - Pollution: cost-benefit Suppose that the cost C...Ch. 0 - Average cost The average cost of producing a...Ch. 0 - Let, , and . Complete the following.
Find.
Find a...Ch. 0 - Evaluate.
Ch. 0 - Use definitions and properties of exponents to...Ch. 0 - Write each of the following as radicals.
Ch. 0 - Simplify each of the following so that only...Ch. 0 - Simplify the following radical expressions and...Ch. 0 - Given the expression, complete the following.
Find...Ch. 0 - Expressusing interval notation and graph it....Ch. 0 - Completely factor each of the...Ch. 0 - Identify the quadratic polynomial from among...Ch. 0 - Find.
Ch. 0 - Perform the indicated operations and simplify....Ch. 0 - Simplify.
Ch. 0 - In a nutrition survey of 320 students, the...Ch. 0 - If is invested for x years at compounded...Ch. 0 - Campaign Management
A politician is trying to...Ch. 0 - Campaign Management
A politician is trying to...Ch. 0 - Campaign Management
A politician is trying to...Ch. 0 - Campaign Management
A politician is trying to...

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