28 CHAPTER R Review of Basic Concepts (d) - 3 4 a 2 9b = - 6 36 Multiply numerators. Multiply denominators. = - 1 6 Write in lowest terms; 6 36 = 1 # 6 6 # 6 = 1 6 (h) - 2 3 - 5 9 This is a complex fraction. A complex fraction has a fraction in the numerator, the denominator, or both. = - 2 3 a9 5b a b = a # 1 b ; Multiply by - 9 5, the reciprocal of the divisor - 5 9. = 18 15 Multiply numerators. Multiply denominators. = 6 5 Write in lowest terms; 18 15 = 6 # 3 5 # 3 = 6 5 S Now Try Exercises 51, 57, 73, and 77. (e) -9 0 is undefined. (f ) 0 -12 = 0 This is true because 01-122 = 0. (g) -12 4 = -3 The numbers have different signs, so the quotient is negative. SOLUTION (a) -31-92 = 27 The numbers have the same sign, so the product is positive. (b) 61-92 = -54 (c) -0.0510.32 = -0.015 The numbers have different signs, so the product is negative. Exponents Any collection of numbers or variables joined by the basic operations of addition, subtraction, multiplication, or division (except by 0), or the operations of raising to powers or taking roots, formed according to the rules of algebra, is an algebraic expression. -2x2 + 3x, 15y 2y - 3 , 2m3 - 64, 13a + b24 Algebraic expressions The expression 23 is an exponential expression, or exponential, where the 3 indicates that three factors of 2 appear in the corresponding product. The number 2 is the base, and the number 3 is the exponent. EXAMPLE 3 Multiplying and Dividing Real Numbers Find each product or quotient where possible. (a) -31-92 (b) 61-92 (c) -0.0510.32 (d) - 3 4 a 2 9b (e) -9 0 (f) 0 -12 (g) -12 4 (h) - 2 3 - 5 9 Exponent: 3 23 = 2 # 2 # 2 = 8 (+)+* Base: 2 Three factors of 2
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