EXAMPLE 1 In-Class Example 1 Identify the base and the exponent in each expression and evaluate. a) 34 b) (3)4 c) 34 Answer: a) base: 3; exponent: 4; 81 b) base: 3; exponent: 4; 81 c) base: 3; exponent: 4; 81 Identify the base and the exponent in each expression and evaluate. a) 24 b) (2)4 c) 24 Solution a) 24 2 is the base, 4 is the exponent. Therefore, 24 2 2 2 2 16. b) (2)4 2 is the base, 4 is the exponent. Therefore, (2)4 (2) (2) (2) (2) 16. c) 24 It may be very tempting to say that the base is 2. However, there are no parentheses in this expression. Therefore, 2 is the base, and 4 is the exponent. To evaluate, 24 1 24 1 2 2 2 2 16 In part c), you must follow the order of operations and evaluate the exponential expression before multiplying by 1. The expressions (a)n and an are not always equivalent: (a)n (a) (a) (a) … (a) ⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩ n factors of a an 1 a a a … a ⎧⎪⎪⎪⎨⎪⎪⎪⎩ n factors of a YOU TRY 1 Identify the base and exponent in each expression and evaluate. a) 53 b) 82 c) a 2 3 b 3 2 Use the Product Rule for Exponents Is there a rule to help us multiply exponential expressions? Let’s rewrite each of the following products as a single power of the base using what we already know: 2 3 3 factors factors 4 factors factors of 2 of 2 of 5 of 5 ⎧⎪⎨⎪⎩ ⎧⎨⎩ ⎧⎨⎩ ⎧⎨⎩ 1) 23 22 2 2 2 2 2 2) 54 53 5 5 5 5 5 5 5 2 2 2 2 2 5 5 5 5 5 5 5 166626663 1664662646663 5 factors of 2 7 factors of 5 25 57 Let’s summarize: 23 22 25, 54 53 57 Do you notice a pattern? When you multiply expressions with the same base, keep the same base and add the exponents. This is called the product rule for exponents. 770 CHAPTER 10 The Rules of Exponents and Polynomials www.mhhe.com/messersmith
messersmith_power_prealgebra_1e_ch4_7_10
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