1. 1 Chapter 5, Section 1 Monomials

2. 2 Monomials defined A monomial is a number, a variable, or the product of numbers and variables. The variables cannot appear in the denominator or under radical signs. A constant is a monomial without variables. A coefficient is the numerical factor of a monomial. The degree of a monomial is the sum of the exponents of its VARIABLES.

3. 3 Powers reviewed For x n, power refers to the NUMBER n that the base is raised to. Remember that x -n equals 1/x n, and so any power with a NEGATIVE power is NOT a monomial, because the variable appears in the denominator.

4. 4 Simplifying Expressions An expression is simplified when it is written without parentheses or negative exponents. Three things we need to remember: Definition of negative exponents: Product of powers property: Quotient of powers property: Note that the result will not necessarily be a monomial.

5. 5 Example 1 Simplify. Assume that s ≠ 0. We will use the quotient of powers property: But we do not allow negative exponents when we simplify, so we use the definition of negative exponents:

6. 6 Other properties of powers Power of a power property: Power of a product property: Power of a quotient: and b ≠ 0 a ≠ 0

7. 7 Example 2 Simplify: This is a power of a power, so we will use that property:

8. 8 Example 3 Simplify This is a power of a product, so we will apply the appropriate property: Note that we usually simplify powers of natural numbers and integers when the result is only 2 or 3 digits.

9. 9 Example 4 Simplify We will use several properties:

10. 10 Example 5 Simplify We will use the power of quotients property:

11. 11 Example 6 Simplify