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Additional info for College Algebra Essentials (4th Edition)
3)-3 c. 1 4-2 d. 3x-6 y4. In Example 3 and Check Point 3, did you notice that 1 1 = 62 and = 42? -2 6 4-2 In general, if a negative exponent appears in a denominator, an expression can be written with a positive exponent using 1 = bn. b-n 24 Chapter P Prerequisites: Fundamental Concepts of Algebra Negative Exponents in Numerators and Denominators If b is any real number other than 0 and n is a natural number, then 1 1 = bn. n and b b-n When a negative number appears as an exponent, switch the position of the base (from numerator to denominator or from denominator to numerator) and make the exponent positive.
20 ͉ ͉ -50 ͉ 5 106. 5 ͉ 2 17 # 18 50 5 108. 18 17 60 6 4 4 110. ͉ -2 ͉ , 17 17 In Exercises 111–120, use the order of operations to simplify each expression. 111. 82 - 16 , 22 # 4 - 3 5#2 - 3 113. 2 [3 - (- 2)]2 2 This algebraic expression gives maximum heart rate in terms of age, a. 94. 6 - 5[8 - (2y - 4)] 97. - (-14x) 99. - (2x - 3y - 6) 101. 13(3x) + [(4y) + (- 4y)] ͉ -3͉ The maximum heart rate, in beats per minute, that you should achieve during exercise is 220 minus your age: 220-a. In Exercises 97–102, write each algebraic expression without parentheses.
002019 n = −3 Move the decimal point ͉−3͉ places, or 3 places, to the left. Move the decimal point ͉−3͉ places, or 3 places, to the left. ● ● ● Check Point 8 Write each number in decimal notation: b. 017 * 10-6 . a. 6 * 109 Converting from Decimal to Scientiﬁc Notation To convert from decimal notation to scientiﬁc notation, we reverse the procedure of Example 8. Converting from Decimal to Scientiﬁc Notation Write the number in the form a * 10n. • Determine a, the numerical factor. Move the decimal point in the given number to obtain a number whose absolute value is between 1 and 10, including 1.