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miller_introductory_algebra_3e_ch1_3

Section 1.5 Multiplication and Division of Real Numbers 87 Observe the pattern for repeated multiplications. 112112 112112112 112112112112 112112112112112 1 112112 112112112 112112112112 1 112112 112112112 1 112112 1 The pattern demonstrated in these examples indicates that • The product of an even number of negative factors is positive. • The product of an odd number of negative factors is negative. 2. Exponential Expressions Recall that for any real number b and any positive integer, n: bn b b b b p b ⎧⎪⎪⎪⎨⎪⎪⎪⎩ n factors of b Be particularly careful when evaluating exponential expressions involving negative numbers. An exponential expression with a negative base is written with parentheses 1224 around the base, such as . 1224, 2 To evaluate the base is used as a factor four times: 1224 122122122122 16 24 If parentheses are not used, the expression has a different meaning: 24 2 1 24. • The expression has a base of 2 (not ) and can be interpreted as 24 1122122122122 16 24 24 • The expression can also be interpreted as the opposite of . 24 12 2 2 22 16 Evaluating Exponential Expressions Example 2 Simplify. a. b. c. d. e. Solution: a. 1522 152152 25 Multiply two factors of 5. b. 52 1152152 25 Multiply 1 by two factors of 5. a 1 2b3 1522 52 (0.4)3 0.43 Concept Connections 7. Without actually computing, determine if the product shown is positive or negative. Explain. 152621420211052 Skill Practice Simplify. 8. 1722 9. 72 10. a 11. 0.23 Classroom Examples: p. 93, Exercises 16, 18, 20, and 22 Answers 7. The product is positive because there is an even number of negative factors. 8. 49 9. 10. 11. 0.008 8 27 49 2 3b3 Avoiding Mistakes The negative sign is not part of the base unless it is in parentheses with the base. Thus, in the expression 52, the exponent applies only to 5 and not to the negative sign. TIP: The following expressions are translated as shown: (3) is read “the opposite of negative three.” 32 is read “the opposite of three squared.” (3)2 is read “negative three, squared.”


miller_introductory_algebra_3e_ch1_3
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