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.
#SIMPLIFYING RATIONAL EXPRESSIONS CALCULATOR PLUS#
However, if there is only a plus sign comes before the grouping, then the parentheses are simply erased.In section 3 of chapter 1 there are several very important definitions, which we have used many times. This means that a minus sign in front of a group will change the addition operation to subtraction and vice versa. When a minus sign is in front of a grouping, it normally affects all the operators inside the parentheses. Therefore, eliminate the parenthesis by multiplying any factor outside the grouping by all terms inside it. In this case, it is impossible to combine terms when they are still in parentheses or any grouping sign.
This expression can be simplified by dividing each term by 2 as Now eliminate the parentheses by multiplying any number outside it Simplify the expression: 2 + 2x įirst work out any terms within brackets by multiplying them out Since both terms in the expression are have same exponents, we combine them Combine the like terms by addition or subtraction.Use the exponent rule to remove grouping if the terms are containing exponents.Remove any grouping symbol such as brackets and parentheses by multiplying factors.To simplify any algebraic expression, the following are the basic rules and steps: Similarly, 7yx and 5xz are unlike terms because each term has different variables. For example, 6x 2and 5x 2 are like terms because they have a variable with a similar exponent. Like terms can sometimes contain different coefficients. Like terms are variables with the same letter and power.A constant is a term that has a definite value.The coefficient is a numerical value used together with a variable.A variable is a letter whose value is unknown in an algebraic expression.Let’s remind ourselves of some of the important terms used when simplifying an expression: