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OBJECTIVES 1.9 Exponential Notation and Order of Operations Slide 1Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aWrite exponential notation for products. bEvaluate exponential notation. cSimplify expressions using the rules for order of operations. dRemove parentheses within parentheses.

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1.9 Exponential Notation and Order of Operations a Write exponential notation for products. Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Some products occur often enough that mathematicians have found it convenient to create a shorter notation, called exponential notation, for them.

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1.9 Exponential Notation and Order of Operations a Write exponential notation for products. Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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EXAMPLE 1.9 Exponential Notation and Order of Operations a Write exponential notation for products. 1 Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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1.9 Exponential Notation and Order of Operations b Evaluate exponential notation. Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. We evaluate exponential notation by rewriting it as a product and then computing the product.

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EXAMPLE 1.9 Exponential Notation and Order of Operations b Evaluate exponential notation. 4 Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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1.9 Exponential Notation and Order of Operations b Evaluate exponential notation. Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. When working with exponential notation, you may be asked to do several things.

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EXAMPLE 1.9 Exponential Notation and Order of Operations c Simplify expressions using the rules for order of operations. 5 Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. There are no parentheses or exponents, so we begin with the third step.

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Title 1.9 Exponential Notation and Order of Operations Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1. Do all calculations within parentheses ( ), brackets [ ], or braces { } before operations outside. 2. Evaluate all exponential expressions. 3. Do all multiplications and divisions in order from left to right. 4. Do all additions and subtractions in order from left to right.

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EXAMPLE 1.9 Exponential Notation and Order of Operations c Simplify expressions using the rules for order of operations. 6 Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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EXAMPLE 1.9 Exponential Notation and Order of Operations c Simplify expressions using the rules for order of operations. 8 Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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EXAMPLE 1.9 Exponential Notation and Order of Operations c Simplify expressions using the rules for order of operations. 10 Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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1.9 Exponential Notation and Order of Operations c Simplify expressions using the rules for order of operations. Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. In order to find the average of a set of numbers, we use addition and then division. The fraction bar acts as a pair of grouping symbols, so we are using order of operations when we compute an average.

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1.9 Exponential Notation and Order of Operations d Remove parentheses within parentheses. Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. When parentheses occur within parentheses, we can make them different shapes, such as [ ] (also called “brackets”) and { } (also called “braces”). All of these have the same meaning. When parentheses occur within parentheses, computations in the innermost ones are to be done first.

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EXAMPLE 1.9 Exponential Notation and Order of Operations d Remove parentheses within parentheses. 13 Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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