EXAMPLE 1 In-Class Example 1 Simplify using the rules of exponents. Assume that the variables do not equal zero. The answer should contain only positive exponents. a) (11z)2 b) 23 c) (8c9)(7c3) d) 78 76 e) 25 34 f) an 5 b 3 g) w7 w5 h) 80 30 i) 109 108 101 Answer: a) 121z2 b) 1 8 c) 56c12 d) 49 e) 32 81 f) n3 125 g) 1 w2 h) 2 i) 1 100 Simplify using the rules of exponents. Assume that the variables do not equal zero. The answer should contain only positive exponents. a) (3y)4 b) 26 c) (7k10)(2k2) d) 89 87 e) 24 52 f) a x 10 b 3 g) m8 m3 h) 90 50 i) 104 106 103 Solution a) Here we have a quantity raised to a power. So, use the power rule. (3y)4 34 y4 81y4 b) 26 1 26 1 64 c) To simplify (7k10)(2k2), we use the product rule because this is the product of two expressions. (7k10)(2k2) (14)(k10 k2) Multiply the coeffi cients, and multiply the variables. 14k102 Apply the product rule. 14k12 Add the exponents. d) 89 87 is the quotient of two expressions with the same base. Therefore, we can use the quotient rule. Subtract the exponents, keep the base the same, and simplify. 89 87 897 82 64 e) Can we simplify 24 52 using the quotient rule? No! The bases are not the same. We must evaluate 24 and 52 separately. 24 52 16 25 f) We use the power rule for a quotient to simplify a x 10 b 3 . a x 10 b 3 x3 103 x3 1000 g) Because m8 m3 is the quotient of two expressions with the same base, use the quotient rule. m8 m3 m8(3) m83 m5 Now, write m5 with a positive exponent. m5 1 m5 Write down the steps as you are reading the example. 782 CHAPTER 10 The Rules of Exponents and Polynomials www.mhhe.com/messersmith
messersmith_power_prealgebra_1e_ch4_7_10
To see the actual publication please follow the link above