Section 1.6 Multiplication and Division of Real Numbers 65 1224, 2 TIP: The following expressions 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: • The expression has a base of 2 (not ) and can be interpreted as 24 2 1 24. 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. 1522 52 10.423 0.43 a. b. c. d. e. a 1 2 3 b Solution: a. Multiply two factors of 5. b. Multiply 1 by two factors of 5. c. Multiply three factors of 0.4. d. Multiply 1 by three factors of 0.4. 1 2 1522 152152 25 52 1152152 25 10.423 10.4210.4210.42 0.064 0.43 110.4210.4210.42 0.064 a 1 2 3 a b 1 2 b a 1 2 b a 1 2 b 1 8 e. Multiply three factors of . Skill Practice Simplify. 7. 8. 72 9. 10. 0.23 a 2 3 3 b 1722 1a 1a 3. Division of Real Numbers Two numbers are reciprocals if their product is 1. For example, are reciprocals because 12 1 . Symbolically, if a is a nonzero real number, then the reciprocal of a is because a 1 .This definition also implies that a number 72 and its reciprocal have the same 27 sign. The Reciprocal of a Real Number Let a be a nonzero real number.Then, the reciprocal of a is . 1a 27 and 72 Recall that to subtract two real numbers, we add the opposite of the second number to the first number. In a similar way, division of real numbers is defined in terms of multiplication.To divide two real numbers, we multiply the first number by the reciprocal of the second number. are translated as: : opposite of negative 3 : opposite of 3 squared 132 32 1322: negative 3, squared 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. Answers 7. 49 8. 9. 10. 0.008 8 27 49
miller_beginning_intermediate_algebra_4e_ch1_3
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