Section 2.4 Multiplication of Fractions and Applications 125 Example 5 3 Solution: 3 Simplifying Expressions 2 a. With an exponent of 3, multiply 3 factors of the base. Multiply the numerators. Multiply the denominators. b. 2 a 2 1 2 parentheses. Simplify. a 2 15 Multiply fractions within parentheses. Square by multiplying times itself. 101 10, 102 100, 1 10 2 In Section 1.7 we learned to recognize powers of 10.These are and so on. In this section, we learn to recognize the powers of one-tenth, that is, raised to a whole-number power. For example, consider the following expressions. 1 2 3 4 From these examples, we see that a power of one-tenth results in a fraction with a 1 in the numerator. The denominator has a 1 followed by the same number of zeros as the exponent on the base of 3. Area of a Triangle Recall that the area of a rectangle with length l and width w is given by w l A l w 1 10. a 1 10 b 1 10 1 10 1 10 1 10 1 10,000 a 1 10 b 1 10 1 10 1 10 1 1000 a 1 10 b 1 10 1 10 1 100 a 1 10 b 1 10 1 10 1 100 1 10 1 10 1 10 a 1 10 b Perform the multiplication within the 3 4 b 15 5 3 1 42 b 8 125 2 2 2 5 5 5 a2 5 b 2 5 2 5 2 5 Simplify. a. b. a 2 15 3 4 b a2 5 b Skill Practice Simplify.Write the answer as a fraction. 2 6 8. 9. aAnswers 8. 9. 1 1000 16 9 5 1 12 3 b a4 3 b
miller_basic_college_math_3e_ch1_3
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