OBJECTIVES

1.9 Exponential Notation and Order of Operations

aSolve applied problems

involving addition, subtraction, multiplication, or division of whole numbers.

Slide 1Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

a Write exponential notation for products.b Evaluate exponential notation.c Simplify expressions using the rules for order of

operations.d Remove parentheses within parentheses.

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.

1.9 Exponential Notation and Order of Operations

a Write exponential notation for products.

Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE

1.9 Exponential Notation and Order of Operations

a Write exponential notation for products.

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Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

1.9 Exponential Notation and Order of Operations

b Evaluate exponential notation.

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We evaluate exponential notation by rewriting it as a product and then computing the product.

EXAMPLE

1.9 Exponential Notation and Order of Operations

b Evaluate exponential notation.

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1.9 Exponential Notation and Order of Operations

b Evaluate exponential notation.

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When working with exponential notation, you may be asked to do several things.

EXAMPLE

1.9 Exponential Notation and Order of Operations

c Simplify expressions using the rules for order of operations.

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There are no parentheses or exponents, so we begin with the third step.

Title

1.9 Exponential Notation and Order of Operations

cSimplify expressions using the rules for order of operations.

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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.

EXAMPLE

1.9 Exponential Notation and Order of Operations

c Simplify expressions using the rules for order of operations.

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EXAMPLE

1.9 Exponential Notation and Order of Operations

c Simplify expressions using the rules for order of operations.

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EXAMPLE

1.9 Exponential Notation and Order of Operations

c Simplify expressions using the rules for order of operations.

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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.

1.9 Exponential Notation and Order of Operations

d Remove parentheses within parentheses.

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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.

EXAMPLE

1.9 Exponential Notation and Order of Operations

d Remove parentheses within parentheses.

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