section concepts 2.2 exponents: multiplying and dividing common bases copyright (c) the mcgraw-hill...
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Section
Concepts
2.2 Exponents: Multiplying and Dividing Common Bases
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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
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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
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For each expression, identify the exponent and base. Then evaluate the expression.
a. b. c.
1
ExampleSolution:
1 Evaluating Expressions with Exponents
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Expression Base Exponent Result
a.
b.
c.
Section 2.2 Exponents: Multiplying and Dividing Common Bases
1. Review of Exponential Notation
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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
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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)
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a.
b.
ExampleSolution:
2 Evaluating Expressions with Exponents
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c.
d.
Example 3 Evaluating Expressions with Exponents
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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)
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b.
Evaluate the expression for and
ExampleSolution:
3 Evaluating Expressions with Exponents
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c.
d.
Evaluate each expression for and
Section 2.2 Exponents: Multiplying and Dividing Common Bases
3. Multiplying and Dividing Common Bases
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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
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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