To multiply factors having the same base add the exponents.įor any rule, law, or formula we must always be very careful to meet the conditions required before attempting to apply it. These laws are derived directly from the definitions.įirst Law of Exponents If a and b are positive integers and x is a real number, then Now that we have reviewed these definitions we wish to establish the very important laws of exponents. Upon completing this section you should be able to correctly apply the first law of exponents. MULTIPLICATION LAW OF EXPONENTS OBJECTIVES We just do not bother to write an exponent of 1. It is also understood that a written numeral such as 3 has an exponent of 1. This can be very important in many operations. ![]() When we write a literal number such as x, it will be understood that the coefficient is one and the exponent is one. ![]() Many students make the error of multiplying the base by the exponent.For example, they will say 3 4 = 12 instead of the correct answer, Note that only the base is affected by the exponent. Unless parentheses are used, the exponent only affects the factor directly preceding it. From using parentheses as grouping symbols we see thatĢx 3 means 2(x)(x)(x), whereas (2x) 3 means (2x)(2x)(2x) or 8x 3. Note the difference between 2x 3 and (2x) 3. An exponent is usually written as a smaller (in size) numeral slightly above and to the right of the factor affected by the exponent.Īn exponent is sometimes referred to as a "power." For example, 5 3 could be referred to as "five to the third power." Make sure you understand the definitions.Īn exponent is a numeral used to indicate how many times a factor is to be used in a product. When naming terms or factors, it is necessary to regard the entire expression.įrom now on through all algebra you will be using the words term and factor. Rules that apply to terms will not, in general, apply to factors. It is very important to be able to distinguish between terms and factors. When an algebraic expression is composed of parts to be multiplied, these parts are called the factors of the expression. In 2x + 5y - 3 the terms are 2x, 5y, and -3. When an algebraic expression is composed of parts connected by + or - signs, these parts, along with their signs, are called the terms of the expression. Since these definitions take on new importance in this chapter, we will repeat them. ![]() Our calculator delivers instant results, ensuring you don't have to wait unnecessarily.Īlongside the result, the calculator provides an explanation to deepen your understanding of partial fraction decomposition.In section 3 of chapter 1 there are several very important definitions, which we have used many times. The intuitive interface ensures that students and professionals can quickly navigate and obtain results without any hassle. Our calculator undergoes rigorous testing to ensure consistently correct results. ![]() Why Choose Our Partial Fraction Decomposition Calculator? The goal of partial fraction decomposition is to take a complex rational expression and decompose it into simpler fractions that are easier to work with.Ī rational expression has the following form: $$R(x)=\frac $$$. Sometimes these expressions can be quite complex and difficult to work with. Partial fraction decomposition is a method used in algebra and calculus to decompose complex rational expressions into simpler fractions, making them easier to manipulate, especially during integration.Ī rational expression (or a rational function) is a fraction in which the numerator and denominator are polynomials. The calculator will quickly process the expression and display the result of decomposition. Once you've entered the data, click the "Calculate" button. How to Use the Partial Fraction Decomposition Calculator?Įnter the numerator and denominator of a rational expression you wish to decompose. Understanding the basics of partial fraction decomposition is critical when learning higher-level math topics. The Partial Fraction Decomposition Calculator is a handy online tool that helps you decompose rational expressions into simpler fractions.
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