Solution a) 50 1 b) 80 1 80 1 1 1 c) (7)0 1 d) 3(20) 3(1) 3 e) t0 1 f) 5k0 5 k0 5 1 5 g) (11p)0 1 h) To evaluate 90 70, we must remember what the order of operations tells us: Evaluate exponents before adding. Use the order of operations when evaluating exponential expressions. YOU TRY 1 Evaluate. 90 70 1 1 2 a) 90 b) 20 c) (5)0 d) 30(2) e) n0 f) 8v0 g) (7r)0 h) 40 50 2 Use Negative Integers as Exponents So far, we have worked with exponents that are zero or positive. What does a negative exponent mean? Let’s use the product rule to fi nd 23 23. 23 23 23(3) 20 1 Remember that a number multiplied by its reciprocal is 1, and here we have that a quantity, 23, times another quantity, 23, is 1. Therefore, 23 and 23 are reciprocals! This leads to the defi nition of a negative exponent. Definition Negative Exponent: If n is any integer and a and b are not equal to zero, then an 1 an. Did you notice that the signs of the bases do NOT change? EXAMPLE 2 In-Class Example 2 Rewrite each expression with only positive exponents and simplify, if possible. Assume that the variable does not equal zero. a) 33 b) (2)2 c) h5 Answer: a) 1 27 b) 1 4 c) 1 h5 Rewrite each expression with only positive exponents and simplify, if possible. Assume that the variable does not equal zero. a) 23 b) (7)2 c) x6 Solution a) 23 1 23 1 8 b) (7)2 1 (7)2 1 49 c) x6 1 x6 h Notice that a negative exponent does not make the answer negative! www.mhhe.com/messersmith SECTION 10.2 Integer Exponents and the Quotient Rule 777
messersmith_power_prealgebra_1e_ch4_7_10
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