Secti on Concep ts 2.2 Exponents: Multiplying and Dividing Common Bases Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1. Review of Exponential Notation 2. Evaluating Expressions with Exponents 3. Multiplying and Dividing Common Bases 4. Simplifying Expressions with Exponents
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Section
Concepts
2.2 Exponents: Multiplying and Dividing Common Bases
Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
1. Review of Exponential Notation2. Evaluating Expressions with Exponents3. Multiplying and Dividing Common Bases4. Simplifying Expressions with Exponents
Section
Concepts
2.2 Exponents: Multiplying and Dividing Like Bases
Any Homework Questions?
Section 2.2 Exponents: Multiplying and Dividing Common Bases
1. Review of Exponential Notation
Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Recall that an exponent is used to show repeated multiplication of the base.
DEFINITION bn
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Let b represent any real number and n represent a positive integer. Then,
Example Evaluating Expressions with Exponents
Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
For each expression, identify the exponent and base. Then evaluate the expression.
a. b. c.
1
ExampleSolution:
1 Evaluating Expressions with Exponents
Slide 6Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Expression Base Exponent Result
a.
b.
c.
Section 2.2 Exponents: Multiplying and Dividing Common Bases
1. Review of Exponential Notation
Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Note that if no exponent is explicitly written for an expression, then the expression has an implied exponent of 1. For example,
Section 2.2 Exponents: Multiplying and Dividing Common Bases
2. Evaluating Expressions with Exponents
Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
An exponential expression with a negative base is written with parentheses around the base, such asTo evaluate we have:If no parentheses are present, the expressionis the opposite of or equivalently,
Example 2 Evaluating Expressions with Exponents
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Evaluate each expression.
a. b. c. d.
ExampleSolution:
2 Evaluating Expressions with Exponents
(continued)
Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
a.
b.
ExampleSolution:
2 Evaluating Expressions with Exponents
Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
c.
d.
Example 3 Evaluating Expressions with Exponents
Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Evaluate each expression for and
a. b. d.
To evaluate a variable expression;1.Replace the variable(s) with the given value(s).2.Simplify using the Order of Operations Agreement.
c.
ExampleSolution:
3 Evaluating Expressions with Exponents
(continued)
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a.Evaluate the expression for and
ExampleSolution:
3 Evaluating Expressions with Exponents
(continued)
Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
b.
Evaluate the expression for and
ExampleSolution:
3 Evaluating Expressions with Exponents
Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
c.
d.
Evaluate each expression for and
Section 2.2 Exponents: Multiplying and Dividing Common Bases
3. Multiplying and Dividing Common Bases
Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Consider the expressions: and
PROPERTY Multiplication of Like Bases
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Assume that b is a real number and that m and n represent positive integers. Then,
Given multiplication of the same base, keep the base, and add the exponents
PROPERTY Division of Like Bases
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Assume that is a real number and that m and n represent positive integers. Then,
Given division of the same base, keep the base, and subtract the exponents.
Example 4 Simplifying Expressions with Exponents
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Simplify the expressions.
a. b.
Example 5 Simplifying Expressions with Exponents
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Simplify the expressions.
a. b.
Example 6 Simplifying Expressions with Exponents
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Simplify the expressions.
a. b.
Example 7 Simplifying Expressions with Exponents
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a. b.
Simplify the expressions.
Example2.
1
Exponents: Multiplying and Dividing Common Bases
Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
1. Review of Exponential Notation2. Evaluating Expressions with Exponents3. Multiplying and Dividing Common Bases4. Simplifying Expressions with Exponents
Example
You Try:
1. Evaluate each expression
22 A. B.
23
4
2. Evaluate 23a b when a = -2 and b = 4
Example
You Try:
3. Simplify each expression
A. B.43
3
C. 3 4 22 6x y x y D. 5 4
3
12
8
x y
x y
62xx
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