DrDelMathIntermediate Algebra 5th Edition
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Exponents may be any real number. The previous formulas (and more in the next section) show how to manipulate exponential expressions regardless of the type of number in the exponent. These formulas also give meaning to negative exponents. The same rules formulas) for manipulating exponentials with natural number exponents apply to exponentials with integer exponents, non-integer rational exponents, and irrational exponents.
A number in scientific notation like xx.xxx X 10n can be changed to standard notation simply by moving the decimal point in xx.xxx n places and omitting the power of 10. If n is positive the decimal is moved to the right and if n is negative the decimal is moved to the left.
A number in standard notation like xxx.xxx can be changed to scientific notation simply by moving the decimal point in xxx.xxx so that there is one significant digit to the left of the decimal. Count how many places the decimal was moved. If the decimal was moved n places to the right, multiply by 10-n. If the decimal was moved n places to the left, multiply by 10n.
Remember that on the index page for Intermediate Algebra there are links to worked out examples.
To see a few worked out exercises involving scientific notation go HERE.
If you want worked out examples of using the laws of exponents to simplify (or simply change) exponential expressions, try these HERE and HERE and HERE and HERE.
If you understand the previous material you should be able to answer the following questions.
Each of the individually listed exercises should be done. In each of the lists (like 5 -
12) work as many as needed to insure that you understand the concept being illustrated or
utilized. Most of these questions or question types are included in the MyMathLab homework
requirement. If a particular concept is difficult for you, you should study the related
text material and then try to answer some additional questions from the list provided by
the department. In each case you are expected to make an honest adult evaluation of your
understanding of the concept. Your ability to answer these questions is one tool to help
you make that evaluation.
Vocabulary and Concept Check: 1 - 12
Section 5.1 Exercise Set: 1 - 10, 11, 13, 15, 16, 17, 18, 19 - 28, 29 - 48, 49 - 82, 83, 85, 87,
91, 93 - 98, 111 - 120.
If you understand the previous material you should be able to answer the following questions.
Each of the individually listed exercises should be done. In each of the lists (like 5 -
12) work as many as needed to insure that you understand the concept being illustrated or
utilized. Most of these questions or question types are included in the MyMathLab homework
requirement. If a particular concept is difficult for you, you should study the related
text material and then try to answer some additional questions from the list provided by
the department. In each case you are expected to make an honest adult evaluation of your
understanding of the concept. Your ability to answer these questions is one tool to help
you make that evaluation.
Vocabulary and Concept Check: 1 - 10
Section 5.2 Exercise Set: 1 - 15, 16 - 27, 57 - 68, 69, 71, 73, 75, 79, 83.
Do not use a calculator for the scientific notation problems.
If you understand the previous material you should be able to answer the following questions.
Each of the individually listed exercises should be done. In each of the lists (like 5 -
12) work as many as needed to insure that you understand the concept being illustrated or
utilized. Most of these questions or question types are included in the MyMathLab homework
requirement. If a particular concept is difficult for you, you should study the related
text material and then try to answer some additional questions from the list provided by
the department. In each case you are expected to make an honest adult evaluation of your
understanding of the concept. Your ability to answer these questions is one tool to help
you make that evaluation.
Vocabulary and Readiness Check: 1 - 14
Section 5.3 Exercise Set: 1 - 10, 11 - 18, 29 - 36, 37, 38, 39, 43, 44, 45, 49, 55,
61, 63, 71, 97, 98, 109, 110.
HERE are some examples of Long Division of Polynomials.
If you understand the previous material you should be able to answer the following questions.
Each of the individually listed exercises should be done. In each of the lists (like 5 -
12) work as many as needed to insure that you understand the concept being illustrated or
utilized. Most of these questions or question types are included in the MyMathLab homework
requirement. If a particular concept is difficult for you, you should study the related
text material and then try to answer some additional questions from the list provided by
the department. In each case you are expected to make an honest adult evaluation of your
understanding of the concept. Your ability to answer these questions is one tool to help
you make that evaluation.
Vocabulary and Readiness Check: 1 - 6
Section 5.4 Exercise Set: 1 - 12, 17 - 26, 27 - 34, 43, 45, 49, 51, 53, 54, 59, 61,
62, 63, 69, 71, 73, 75, 76, 77, 103, 104, 105.
Division of polynomials is not included in this section of the textbook, so there are some exercises listed HERE. Solutions are on the same page.
When used as a noun the word factor refers to the individual parts of a product. When used as a verb (to factor) it means to write something as a product.
For example, in many arithmetic situations recognizing the number 136 as the product of 8 and 17 is a benefit. In such situations it is customary to claim that to factor 136 as (8)(17) is a simplification. In the same way factorizations of polynomials is usually a simplification. There are several methods for factoring polynomials. No single one of these methods is sufficient for all occassions, but in combination they can yield a factored (simplified) form of seemingly complex polynomials.
The very first step when factoring any polynomial is to identify the GCF of the terms of the polynomial and to write the polynomial as a product with the GCF as one of the factors. The Distributive Property is used to verify that the factorization is correct. A common phrase used to refer to this procedure is "to factor out the GCF".
If you understand the previous material you should be able to answer the following questions.
Each of the individually listed exercises should be done. In each of the lists (like 5 -
12) work as many as needed to insure that you understand the concept being illustrated or
utilized. Most of these questions or question types are included in the MyMathLab homework
requirement. If a particular concept is difficult for you, you should study the related
text material and then try to answer some additional questions from the list provided by
the department. In each case you are expected to make an honest adult evaluation of your
understanding of the concept. Your ability to answer these questions is one tool to help
you make that evaluation.
Vocabulary and Readiness Check: 1 - 16
Section 5.5 Exercise Set: 1, 3, 5, 7, 9 - 23 (As many as you have time for), 25,
27, 29, 30, 31, 32.
Factoring is a SKILL that can be quite helpful. This is one of the few topics in mathematics where practice is really beneficial. Practice by working as many exercises as time permits.
If you understand the previous material you should be able to answer the following questions.
Each of the individually listed exercises should be done. In each of the lists (like 5 -
12) work as many as needed to insure that you understand the concept being illustrated or
utilized. Most of these questions or question types are included in the MyMathLab homework
requirement. If a particular concept is difficult for you, you should study the related
text material and then try to answer some additional questions from the list provided by
the department. In each case you are expected to make an honest adult evaluation of your
understanding of the concept. Your ability to answer these questions is one tool to help
you make that evaluation.
Vocabulary and Readiness Check: 1 - 4
Section 5.6 Exercise Set: 1 - 14 (As many as you have time for.), 15 - 34
(As many as you have time for.), 35 - 42 (As many as you have time for.). Use Method 1
and substitution methods. Don't bother with method 2.
If you understand the previous material you should be able to answer the following questions.
Each of the individually listed exercises should be done. In each of the lists (like 5 -
12) work as many as needed to insure that you understand the concept being illustrated or
utilized. Most of these questions or question types are included in the MyMathLab homework
requirement. If a particular concept is difficult for you, you should study the related
text material and then try to answer some additional questions from the list provided by
the department. In each case you are expected to make an honest adult evaluation of your
understanding of the concept. Your ability to answer these questions is one tool to help
you make that evaluation.
Vocabulary and Readiness Check: 1 - 10
Section 5.7 Exercise Set: 1 - 8, 9 - 16, 17 - 28, 29, 31, 33.
If you understand the previous material you should be able to answer the following questions.
Each of the individually listed exercises should be done. In each of the lists (like 5 -
12) work as many as needed to insure that you understand the concept being illustrated or
utilized. Most of these questions or question types are included in the MyMathLab homework
requirement. If a particular concept is difficult for you, you should study the related
text material and then try to answer some additional questions from the list provided by
the department. In each case you are expected to make an honest adult evaluation of your
understanding of the concept. Your ability to answer these questions is one tool to help
you make that evaluation.
Vocabulary and Readiness Check: 1 - 16
Section 5.8 Exercise Set: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 17, 21, 22,
23, 24, 73, 74, 77.