1 Write A Short Paragraph About Integer Exponents In Particular Add ✓ Solved

1. Write a short paragraph about integer exponents. In particular, address the cases of zero exponents and negative integer exponents. 1a. How do the special products help us factor polynomials?

Give examples. 2. Compare numerical fractions and rational expressions. What is common and what is different about them? Support your answer with examples.

2a. How do we make sure that a rational expression does not get undefined? 3. Compare taking a root and raising to a power. Support your observations with your own examples.

3a. What methods of solving quadratic equations did you learn? What method do you prefer, and in what cases? 2 Table of Contents ABSTRACT ................................................................................................................................ 3 INTRODUCTION ........................................................................................................................

4 THE EXISTING SYSTEM’ PROPBLEMS ........................................................................................... 5 RESEARCH METHODOLOGY ....................................................................................................... 6 ANALYSIS APPROACH ................................................................................................................ 7 DISCUSSION AND CONCLUSION ................................................................................................. 9 REFERENCES .....................................................................................................................

ABSTRACT Most companies and institutions and any place that includes several human resources need a system that manages these resources and organizes their work and affairs, known as enterprise resource planning (ERP). These resources usually include employees or clients within the organization. In this paper, I will study the organization's human resource management system, which is characterized by some generality in performing basic functions and neglecting the special requirements that the organization needs. And I will study the reasons that led to this problem, and I will analyze the requirements necessary to find a solution to this problem. At the end of the paper, an analysis of a new system will be presented that addresses the gaps in the old system.

4 INTRODUCTION Overview Enterprise resource planning is an information system or project that exists to organize and coordinate information related to human resources within the organization, including matters relating to salaries, vacations, employee attendance times, and the organization of dealers with the institution such as customers or clients (Kelle & Akbulutb, 2005). Human resource planning systems provide improvement in the performance of the organization in terms of improving productivity and easily accessing information in a timely manner. These systems reduce dependency on paper and transfer the traditional systems to more sophisticated systems. As well as automating all processes by integrating and coordinating information across all departments (Monk & Wagner, 2013).

Benefits of ERP System - The enterprise planning system provides the continuity of the flow of data within the organization and the ability to manage it and prevent the diversity of places of data preservation and its unification in one place from more than one source (Law & Ngai, 2007). - The enterprise planning system provides a link for all departments of the same organization in one place and saves the data of each of them in one place while providing them with the necessary protection (Chen, 2004). 5 - The ERP system makes the institution more intelligent by providing information at the time of its request, in addition to being easily accessible and presented in an appropriate manner (Parr & Shanks, 2000). - The ERP system reduces human errors because it relies completely on specific models that take custom and pre-prepared data to be saved in one place and benefit from it later while avoiding any human errors (Karande, Jain, & Ghatule, 2012).

THE EXISTING SYSTEM’ PROPBLEMS The new system is a real ERP system but does not perform the main functions required as expected. The current system came as a developmental step for the system that preceded it, but it also did not provide complete solutions.This paper aims to study the current human resource management system for a real institution and to study the reasons for the failure selection of this system, which can be listed in the following points: - Not knowing the old system and not analyzing it in order to purchase a new system that addresses its problems and being content with developing a general system only, and not taking into account the requirements of the institution in particular. - Unavailability of an expert or consultant specialized in studying and analyzing systems within the institution’s information technology 6 department to take his advice in creating or purchasing a new system.

This would bring together all the capabilities required of the new system. - A new system not taken into account The levels of the department's administrative structure, causing problems in approval processes for leave requests, and problems in knowing which department or section the employee works in and his direct manager. RESEARCH METHODOLOGY During our study of the new system, we collected a set of data from the interviews. These interviews included asking questions of the first dealers with this application, who are the employees who work on adding, deleting, modifying and reviewing the human resources data in the organization. The questions were about their satisfaction with the new system and whether it added new things to the old system.

Also, some questions were raised in an interview with the Human Resources Department, and the questions were about the basis and reference that they used to purchase a new system. After performing an analysis of the data we obtained from the interviews, it was found that there are two steps that were not applied, namely not consulting any expert to analyze the old system in order to purchase A new system that matches the old and improves its work with other functions. The second step is to pay attention to the shape and design of a new ERP system, and not to pay attention to its content and the functions that it must provide that meet the needs of the institution. The neglect of the previous steps 7 resulted in two main problems that led to the analysis of this system again, namely the problem of inconsistency of the leave system with the policies of the institution.

Human resources, it does not give the vacation to two levels of management, meaning that he omitted a third level, which is the section level.The second problem is that if an employee applies for a leave, this request may go to a department different from his own, which of course does not contain the employee's name and therefore will not be allowed to leave or to have his required vacation. ANALYSIS APPROACH In this study, a descriptive statistical approach will be adopted to analyze the data obtained and the reason for choosing this approach in order to describe the relationship between variables in a sample or population. This sample consists of the various answers gathered from the aforementioned interviews.

Descriptive statistics allow you to identify and describe any characteristics of the collected data, to simplify and summarize them. Also, the descriptive statistics do not allow access to hypothetical results, but rather real results of the analysis. In order to complete the analysis process and its results, it is clear that the new system needs these functions as major improvements in the system as follows: General Requirements The enhanced application should integrate with the old system and mapping the data needed in the new system. 8 Approval of The Vacation Request This feature enables officials to approve vacations for employees by three levels of authorities, approval by the section manager, then the department manager and finally by the administration.

Permissions The system should provide for the possibility of dividing responsibilities into three stages: public administration, departments and sections, according to the structure of responsibilities in the institution. System Stability The system must provide the ability to move the user between sections of the system easily, while the interfaces of the software system are identical with each other and not differ and remain unified. Import and Export Data The system must be flexible in receiving all kinds of data and merging them into a basic database, and this data includes information about employees, bonus records, or any other related items. The system must also export data in the form of excel or printable reports.

Administrator ERP System This means the existence of an authority that has full permissions in managing the system, and among these permissions is adding a new user, modifying user data, assigning some permissions or preventing them. 9 DISCUSSION AND CONCLUSION The aim of studying the paper was to add some improvements to an existing ERP system. This system was an alternative system to an old previous system for my organization. In this paper, I examined the reasons that led to the inefficiency of the current new system. I listed a bunch of steps that were missing in making the decision to purchase a new system.

Based on that, this paper presented an analysis of the current new system, and based on the information I got from the interview with the administration of the institution and some other departments within it, I concluded improvements to this system in order to serve the orientations and behaviors of the institution. This paper was a critique of a real system and an illustration of the steps that were taken to analyze and develop the alternative system presented as a solution. 10 REFERENCES Chen, P. (2004). Developing Knowledge Management Systems in BPM Context. springer. Karande, S., Jain, V., & Ghatule, A. (2012).

ERP implementation: critical success factors for Indian Universities and higher educational institutions. Pragyaan Journal of Information Technology. Kelle, P., & Akbulutb, A. (2005). The role of ERP tools in supply chain information sharing, cooperation, and cost optimization. International Journal of Production Economics.

Law, C. C., & Ngai, E. W. (2007). An investigation of the relationships between organizational factors, business process improvement, and ERP success. Benchmarking: An International Journal.

Monk, E., & Wagner, B. (2013). Concepts in Enterprise Resource Planning 4th Edition. USA. Parr, A., & Shanks, G. (2000). A model of ERP project implementation. springer.

Paper for above instructions

Integer Exponents

Integer exponents represent the power to which a base is raised, and they play a significant role in algebraic expressions. When dealing with integer exponents, two specific cases warrant particular attention: zero exponents and negative integer exponents. The rule for zero exponents states that any non-zero number raised to the power of zero equals one (e.g., \(a^0 = 1\), where \(a \neq 0\)). This rule is essential because it maintains a consistent framework across exponentiation and facilitates computations (Stein, 2018). Negative exponents, on the other hand, indicate the reciprocal of the base raised to the opposing positive exponent (e.g., \(a^{-n} = \frac{1}{a^n}\)). For instance, \(2^{-3} = \frac{1}{2^3} = \frac{1}{8}\). The understanding of these rules is essential for simplifying algebraic expressions and solving equations.
In terms of factoring polynomials, special products—such as the difference of squares, perfect squares, and the sum of cubes—provide formulas that simplify the factorization process. For example, the difference of squares states that \(a^2 - b^2 = (a - b)(a + b)\). Using this rule, one can factor expressions like \(x^2 - 16\) into \((x - 4)(x + 4)\). Additionally, recognizing these special forms can streamline polynomial long division and simplify rational expressions, enabling easier manipulation of larger algebraic expressions (Rosenberg, 2019).

Numerical Fractions and Rational Expressions

Numerical fractions and rational expressions share a common structural characteristic in that they both represent a ratio of two quantities. However, they differ in their forms. A numerical fraction is a ratio involving specific numbers, such as \(\frac{3}{4}\), whereas a rational expression generally includes variables in its numerator and/or denominator, such as \(\frac{x + 2}{x - 5}\) (Bittinger, 2013).
One critical issue is that while numerical fractions are defined for all real numbers (except zero in the denominator), rational expressions may be undefined for specific values of the variable. For example, the rational expression \(\frac{x + 1}{x - 2}\) is undefined when \(x = 2\) since it leads to division by zero. Therefore, identifying restrictions on the variables is crucial when working with rational expressions in order to ensure that they remain defined (Nored, 2016).
To prevent a rational expression from being undefined, one must ascertain the values that would make the denominator equal to zero and exclude these from the domain of the expression. For instance, in the expression \(\frac{2x + 3}{x^2 - 4}\), we find that \(x^2 - 4\) factors to \((x - 2)(x + 2)\), leading to restrictions \(x \neq 2\) and \(x \neq -2\) (Friedman, 2010).

Root Taking vs. Raising to a Power

The operations of taking roots and raising numbers to powers are fundamental aspects of mathematics, both related to exponents but serving distinct functions. Raising to a power signifies multiplying a number by itself a certain number of times—e.g., \(3^4 = 3 \times 3 \times 3 \times 3 = 81\). This operation has many applications, particularly in algebraic contexts such as solving polynomial equations (Ahlfors, 1979).
On the other hand, taking roots—specifically square roots—can be thought of as the inverse of raising to a power. For instance, \(\sqrt{81} = 9\) because \(9^2 = 81\). Generally, the square root of a number \(a\) returns a value \(b\) such that \(b^2 = a\). This duality can also be generalized to other roots; for instance, taking cube roots and fourth roots demonstrates how both operations communicate essential properties of numbers. For example, the cube root of \(27\) results in \(3\) because \(3^3 = 27\) (Meyer, 2015).
In various algebraic contexts, knowing when to apply exponentiation versus root extraction is useful for problem-solving. For example, solving the quadratic equation \(x^2 - 16 = 0\) can involve raising to the power of two or taking square roots as alternative methods. Techniques employed can often depend on personal preference or ease of computation (Becker, 2011).

Solving Quadratic Equations

Several methods exist for solving quadratic equations, each bearing unique advantages. The primary methods include factoring, using the quadratic formula, and completing the square. When a quadratic equation can be factored neatly, factoring is often the most straightforward approach. For instance, in the equation \(x^2 + 5x + 6 = 0\), one can quickly identify that it factors into \((x + 2)(x + 3) = 0\), yielding \(x = -2\) and \(x = -3\) (Cohen, 2017).
When factoring is non-trivial or in cases where the quadratic does not easily factor, the quadratic formula, \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), becomes invaluable. For instance, in the equation \(2x^2 + 4x + 2 = 0\), employing the quadratic formula would yield solutions by substituting \(a = 2\), \(b = 4\), and \(c = 2\) into the formula (Swokowski & Cole, 2011).
Completing the square is a third method, which is particularly useful in understanding the vertex form of a quadratic equation—this mode of operation can visually demonstrate the maximum or minimum of a parabola represented by the equation. Ultimately, preference for a technique often rests on the specifics of the quadratic at hand or the solver's comfort level with each method (Kirk, 2008).

Conclusion

In conclusion, the mathematical principles surrounding integer exponents, rational expressions, and quadratic equations are vital components of higher mathematics. From understanding exponents—such as the functions of zero and negative integers—to recognizing the differences between numerical fractions and rational expressions, a strong foundation in these concepts proves indispensable. Applying different methods in solving quadratic equations also highlights the robust nature of algebra, enabling flexibility in problem-solving.

References

1. Ahlfors, L. V. (1979). Complex Analysis. McGraw Hill.
2. Becker, K. (2011). Quadratic Equations and Functions. USA: Educational Publishing.
3. Bittinger, M. L. (2013). Algebra and Trigonometry. Pearson Education.
4. Cohen, C. (2017). Introduction to Algebra. Springer.
5. Friedman, M. (2010). Introductions to Rational Expressions. Wiley.
6. Kirk, A. (2008). Elementary Algebra. Brookfield: TSI Publications.
7. Meyer, R. (2015). Understanding Square Roots. Academic Press.
8. Nored, J. (2016). Prealgebra and Introduction to Algebra. Pearson Education.
9. Rosenberg, I. (2019). Factoring Polynomials: The Basics. College Algebra Review.
10. Stein, M. (2018). Exponents and Their Properties. New York: Academic Publications.