Section 1-2: Exponents and Order of Operations Objectives: (1) To Simplify and evaluate formulas and expressions (2) To add, subtract, multiply and divide expression with exponents (3) To simplify and evaluate expressions with grouping symbols

Definitions To simplify a numerical expression, you replace it with its simplest name. An exponent tells how many times a number, the base, is used as a factor. A power has two parts, a base and an exponent You evaluate an algebraic expression by substituting a given number for each variable. Then Simplify the numerical expression using the order of operations.

Order of Operations Please, excuse my dear Aunt Sally. Please Excuse Parenthesis ( ), or other grouping symbols like braces { } and brackets [ ] Excuse Exponents My Multiplication Dear Division Aunt Addition Sally Subtraction

Order of Operations This is the order in which you must begin evaluating expressions. Multiplication and division are inverse operations (they undo each other) and therefore are done by the order in which they appear in the expression Addition and subtraction are inverse operations and are done by the order in which they appear in the expression

Simplifying a Numerical Expression Which operation appears 1st? Exponents! Find 32 Now, multiplication Subtraction comes first because add/subt is done by whichever comes first in the expression And Add 18 is the simplified answer

Evaluating an Algebraic Expression Evaluate 3a – 23 ÷ b a = 7 b = 4 3(7) – 23 ÷ (4) 3(7) – 8 ÷ 4 21 – 2 19 First replace all variables with their numerical counterparts with parenthesis Exponents first Multiplication AND Division Subtraction All Done

Real World Examples (Word Problems) Your favorite pair of sneakers are on sale for $59.00. There is a 6% sales tax in your state with any purchase. Find the total cost of the sneakers. Use the following formula: C = p + r• p C is the cost P is the price R is the sales tax rate

Real World Examples (Word Problems) C = 59 + (0.06)(59) C = 59 + 3.54 C = 62.54 You’re done! Replace with actually values. Order of operations tells us multiply first. Now add Easy, right?

Simplifying an Expression with Parenthesis Simplify 15(13 – 7) ÷ (8 – 5) 15(6) ÷ (3) 90 ÷ 3 30 All done! Simplify the stuff inside the parenthesis first. Remember that no symbol between a number outside a parenthesis and the parenthesis means multiply Now divide

Evaluating Expressions with Exponents Evaluate each expression for c = 15 and d = 12 (cd)2 [(15)(12)]2 (180)2 32,400 Substitute 15 for c and 12 for d Simplify the parenthesis first Now raise it to the exponent

Evaluating Expressions with Exponents Evaluate each expression for c = 15 and d = 12 cd2 (15)(12)2 (15)(144) 2,160 Substitute 15 for c and 12 for d Raise 12 to the 2nd power first Now multiply

Simplifying an Expression Simplify 2[(13 – 7)2 ÷ 3] 2[(6)2 ÷ 3] 2[36 ÷ 3] 2 [ 12 ] 24 And you are done! 1st simplify the parenthesis 2nd Simplify the power Simplify the brackets Multiply

Real World Problem Solving: Urban Planning A neighborhood association turned a vacant lot into a park. The park is shaped like the trapezoid to the right. Use the formula to find the area of the lot. b1 = 100 ft h = 130 ft b2 = 200 ft

Real World Problem Solving: Urban Planning We know: The area of the park is 19,500 ft2 Substitute 130 for h, 100 for b1 and 200 for b2 Simplify the numerator Simplify the fraction Multiply