10.1 The Product Rule and Power Rules What are your objectives for Section 10.1? How can you accomplish each objective? 1 Evaluate Exponential Expressions • Write the defi nition of exponential expression in your own words, using the words base and exponent. • Complete the given example on your own. • Complete You Try 1. 2 Use the Product Rule for Exponents • Learn the property for the Product Rule, and write an example in your notes. • Complete the given example on your own. • Complete You Try 2. 3 Use the Power Rule (am)n amn • Learn the property for the Basic Power Rule, and write an example in your notes. • Complete the given example on your own. • Complete You Try 3. 4 Use the Power Rule (ab)n anbn • Learn the property for the Power Rule for a Product, and write an example in your notes. • Complete the given example on your own. • Complete You Try 4. 5 Use the Power Rule aa b b n an bn, where b 0 • Learn the property for the Power Rule for a Quotient, and write an example in your notes. • Complete the given example on your own. • Complete You Try 5. • Write the summary for the product and power rules of exponents in your notes, and be able to apply them. Read the explanations, follow the examples, take notes, and complete the You Trys. 1 Evaluate Exponential Expressions Recall from Chapter 1 that exponential notation is used as a shorthand way to represent a multiplication problem. For example, 3 3 3 3 3 can be written as 35. Definition An exponential expression of the form an, where a is any real number and n is a positive integer, is equivalent to a a a … a. We say that a is the base and n is the exponent. ⎧⎪⎪⎨⎪⎪⎩ n factors of a We can also evaluate an exponential expression. www.mhhe.com/messersmith SECTION 10.1 The Product Rule and Power Rules 769
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