108 Chapter 2 Integers and Algebraic Expressions Multiplying Several Factors Example 3 Multiply. a. 122 152 172 b. 142 122 112 152 Solution: a. 122 152 172 This product has an odd number of negative factors. 70 The product is negative. b. 142 122 112 152 This product has an even number of negative factors. 40 The product is positive. 3. Exponential Expressions Be particularly careful when evaluating exponential expressions involving negative numbers. An exponential expression with a negative base is written with parentheses around the base, such as 1324. To evaluate 1324, the base 3 is multiplied 4 times: 1324 132 132 132 132 81 If parentheses are not used, the expression 34 has a different meaning: • The expression 34 has a base of 3 (not 3) and can be interpreted as 1 34. Hence, 34 1 132 132 132 132 81 • The expression 34 can also be interpreted as “the opposite of 34. ” Hence, 34 13 3 3 32 81 Simplifying Exponential Expressions Example 4 Simplify. a. 1422 b. 42 c. 1523 d. 53 Solution: a. 1422 142 142 The base is 4. 16 Multiply. b. 42 142 142 The base is 4. This is equal to 1 42 1 142 142. 16 Multiply. c. 1523 152152152 The base is 5. 125 Multiply. d. 53 152 152 152 The base is 5. This is equal to 1 53 1 152152152. 125 Multiply. Skill Practice Multiply. 13. 132 142 182 112 14. 112 142 162 152 Skill Practice Simplify. 15. 1522 16. 52 17. 1223 18. 23 Avoiding Mistakes In Example 4(b) the base is positive because the negative sign is not enclosed in parentheses with the base. Answers 13. 96 14. 120 15. 25 16. 25 17. 8 18. 8
miller_prealgebra_2e_ch1_3
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