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6.2A Apply Properties of Rational Exponents Algebra II Review of Properties of Exponents from section 5.1 am * an = am+n (am)n = amn (ab)m = ambm These all work a-m = 1 a a for rational a = am-n (fraction) a a = exponents as b b well as integer exponents. m m n m m m Ex. 1 : Simplify. (no decimal answers) 61/2 * 61/3 = 61/2 + 1/3 = 63/6 + 2/6 = 65/6 b. (271/3 * 61/4)2 = (271/3)2 * (61/4)2 = (3)2 * 62/4 = 9 * 61/2 a. (43 * 23)-1/3 = (43)-1/3 * (23)-1/3 = 4-1 * 2-1 c. =¼ *½ = 1/ 8 1 3 d. 18 4 1 94 = 18 9 3 4 3 4 = 18 9 3 4 = 2 3 4 ** All of these examples were in rational exponent form to begin with, so the answers should be in the same form! Ex 2: Simplify. 3 25 5= a. 3 3 Ex 3: Write the expression in simplest form. 25 5 3 a. = 125 = 5 4 64 4 = 16 4 = 4 16 4 4 = 24 4 3 32 3 4 b. = 3 = 3 32 4 b. 4 7 8 8 = 2 4 = ** If the problem is in radical form to begin with, the answer should be in radical form as well. = 4 4 7 8 7 42 4 8 2 4 = 4 14 2 Can’t have a tent in the basement! 4 = 14 4 16 Ex 4: Perform the indicated operation a. 5(43/4) – 3(43/4) = 2(43/4) b. 3 81 3 3 = 3 27 3 3 3 = 33 3 3 3 = 23 3 c. 3 625 3 5 = 3 125 5 3 5 3 3 = 5 5 5 3 =6 5 If the original problem is in radical form, the answer should be in radical form as well. If the problem is in rational exponent form, the answer should be in rational exponent form. 6.2B Simplifying Expressions with Variables Ex. 1 x2 x a. b. c. d. 6 x 11 y13 4 7 r8 4 x 6 y 11 x y 2 r4 r4 4 r 4 4 r 4 r r r 2 Ex 2: Simplify the Expression. Assume all variables are positive. a. 27z 27 z 3z 3 9 3 3 (16g4h2)1/2 = 161/2g4/2h2/2 = 4g2h b. c. 5 x5 y10 x y2 5 5 x5 y10 9 3 d. 18rs 2 3 1 4 3 6r t 3r 3 4 1 2 3 3 3r s t 1 4 2 3 s t3 Ex. 3 Perform the indicated operation. Assume all variables are positive. a.)18 u 11 u 3 3 4 2/3 b.)15a b 8a b 4 2/3 c.)10 5s 3s 80 s 4 7 4 3 Assignment Ex. 4 Write the expression in simplest form. 3 a.) 104 4 10 b.) 4 27