1. § 1.9 Exponents, Parentheses and Order of Operations

2. Angel, Elementary Algebra, 7ed 2 Exponents In the expression 3 4, the 3 is called the base, and the 4 is called the exponent. exponent 3434 base 3 4 is read “3 to the fourth power” and means 3·3·3·3 = 3 4 = 81 4 factors of 3 Note that x + x + x + x = 4x and x ·x ·x ·x = x 4

3. Angel, Elementary Algebra, 7ed 3 – x 2 vs. (-x) 2 An exponent refers only to the number or letter that directly precedes it unless parentheses are used to indicate otherwise. – x 2 = -(x)(x) ( – x) 2 = ( – x)(-x) = x 2 Example: – 5 2 = – (5)(5) = – 25 ( – 5) 2 = ( - 5)(-5) = 25

4. Angel, Elementary Algebra, 7ed 4 Order of Operations To evaluate mathematical expressions, use the following order: 1.First, evaluate the information within parentheses ( ), brackets  , or braces  .These are grouping symbols, for they group information together. A fraction bar, —, also serves as a grouping symbol. If the expression contains nested parentheses (one pair of parentheses within another pair), evaluate the information in the innermost pair first.

5. Angel, Elementary Algebra, 7ed 5 Order of Operations 2.Next, evaluate all the exponents. 3.Next, evaluate all the multiplications and divisions in the order in which they occur, working from left to right. 4.Finally, evaluate all additions or subtractions in the order in which they occur, working from left to right.

6. Angel, Elementary Algebra, 7ed 6 Order of Operations Evaluate: 4 + (4 2 – 13) 4 – 3 = exponent inside parentheses parentheses exponent addition subtraction 4 + (16 – 13) 4 – 3 = 4 + (3) 4 – 3 = 4 + 81 – 3 = 85 – 3 = 82 Steps Taken

7. Angel, Elementary Algebra, 7ed 7 Order of Operations Evaluate: parentheses, subtraction division Two steps combined exponent subtraction Two steps combined subtraction Two steps combined exponent 48 division

8. Angel, Elementary Algebra, 7ed 8 Expressions Containing Variables Evaluate: 3(x – 2) when x = 5 This means to substitute 5 for x. 5 3(5 – 2) = 3(3) = 9 Evaluate: 3n 2 (2n – 1) + 5 when n = -4 44 3( – 4) 2 [2( – 4) – 1] + 5 = 3(16)( – 8 – 1) + 5 = 3(16)( – 9) + 5 = – 432 + 5 = – 427