7: Exponents and Polynomials
- Page ID
- 137928
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- 7.1: Multiplication with Exponents
- In this section, we will begin working with variable expressions containing exponents. Remember that an exponent indicates repeated multiplication of the same quantity. You have seen that when you combine like terms by adding and subtracting, you need to have the same base with the same exponent. But when you multiply and divide, the exponents may be different, and sometimes the bases may be different, too. We’ll derive the properties of exponents by looking for patterns in several examples.
- 7.2: Division with Exponents
- In this section, we will look at the exponent properties for division. A special case of the Quotient Property is when the exponents of the numerator and denominator are equal. It leads us to the definition of the zero exponent, which states that if a is a non-zero number, then a^0 = 1. Any nonzero number raised to the zero power is 1. The quotient to a power property of exponents states that to raise a fraction to a power, you raise the numerator and denominator to that power.
- 7.3: Adding and Subtracting Polynomials
- In this section, we will work with polynomials that have only one variable in each term. The degree of a polynomial and the degree of its terms are determined by the exponents of the variable. Working with polynomials is easier when you list the terms in descending order of degrees. When a polynomial is written this way, it is said to be in standard form. Adding and subtracting polynomials can be thought of as just adding and subtracting like terms.
- 7.4: Multiplying Polynomials
- In this section, we will begin multiplying polynomials with degree one, two, and/or three. Just like there are different ways to represent multiplication of numbers, there are several methods that can be used to multiply a polynomial by another polynomial. The Distributive Property is the first method that you have already encountered and used to find the product of any two polynomials.