1. Algebra 1A Vocabulary 1-2 Review Problem 5 Suppose you draw a segment from any one vertex of a regular polygon to the other vertices. A sample for a regular hexagon is shown above. Use the table to find a pattern. What is a rule for the number of nonoverlapping triangles formed?

2. Problem 5 Number of Sides of PolygonNumber of Triangles  Give a rule in words to find the number of nonoverlapping triangles in a polygon.  Write an algebraic expression for the number of nonoverlapping triangles in a polygon that has n sides.

3. Review What is a variable? What does a numerical expression contain? What does an algebraic expression contain? Give an example of an operation.

4. An exponent is a shorthand notation for repeated multiplication. 3 3 3 3 3 3 is a factor 5 times Using an exponent, this product can be written as exponent base Exponents

5. This is called exponential notation. The exponent, 5, indicates how many times the base, 3, is a factor. exponent base Read as “three to the fifth power” or “the fifth power of three.” 3 3 3 3 3 3 is a factor 5 times Exponential Notation

6. Simplify You simplify a numerical expression when you replace it with its single numerical value. Example: To simplify a power, you replace it with its simplest name, For example, The simplest being 81.

7. Sample Problems 1. What is the simplest form of each expression?

8. Order of Operations When simplifying algebraic expressions with more than one operation, you have to make a decision about what order to perform the operations. For example,

9. 1. Perform all operations within parentheses ( ), brackets [ ], or other grouping symbols such as fraction bars, starting with the innermost set. 2.Simplify powers. 3.Multiply or divide in order from left to right. 4.Add or subtract in order from left to right. Rules for Order of Operations

10. Sample Problems 1. What is the simplified form of each expression?