Simplify using the power rule. a) (38)4 b) (n3)7 c) ((f )4)3 Solution a) (38)4 38 4 332 b) (n3)7 n3 7 n21 c) ((f )4)3 (f )4 3 (f )12 YOU TRY 3 Simplify using the power rule. a) (54)3 b) ( j6)5 c) ((2)3)2 4 Use the Power Rule (ab)n anbn We can use another power rule to simplify an expression such as (5c)3. We can rewrite and simplify (5c)3 as 5c 5c 5c 5 5 5 c c c 53c3 125c3. To raise a product EXAMPLE 3 In-Class Example 3 Simplify using the power rule. a) (46)3 b) (m2)5 c) (q8)7 Answer: a) 418 b) m10 c) q56 This property demonstrates to a power, raise each factor to that power. how you can distribute an exponent to the bases if the bases are being multiplied. Property Power Rule for a Product Let a and b be real numbers, and let n be a positive integer. Then, (ab)n anbn To raise a product to a power, raise each factor to that power. EXAMPLE 4 In-Class Example 4 Simplify each expression. a) (4x)3 b) a 1 2 ub 4 c) (3g)3 d) (2w4)5 e) 2(8mn)2 Answer: a) 64x3 b) 1 16 u4 c) 27g3 d) 32w20 e) 128m2n2 Notice that (ab)n anbn is different from (a b)n. (a b)n an bn. Simplify each expression. a) (9y)2 b) a1 4 tb 3 c) (5c2)3 d) 3(6ab)2 Solution a) (9y)2 92y2 81y2 b) a1 4 tb 3 a1 4 b 3 t3 1 64 t3 c) (5c2)3 53 (c2)3 125c2 3 125c6 d) 3(6ab)2 362 (a)2 (b)2 The 3 is not in parentheses; therefore, it will not be squared. 3(36a2b2) 108a2b2 YOU TRY 4 Simplify. a) (k4)7 b) (2k10m3)6 c) (r2s8)3 d) 4(3tu)2 772 CHAPTER 10 The Rules of Exponents and Polynomials www.mhhe.com/messersmith
messersmith_power_prealgebra_1e_ch4_7_10
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