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7.2 Properties of Rational Exponents Algebra 2 Mrs. Spitz Spring 2009 Objectives/Assignment Use properties of rational exponents to evaluate and simplify expressions. Use properties of rational exponents to solve real-life problems, such as finding the surface area of a mammal. Assignment: pp. 411-412 #5-81 every 3rd Review of Properties of Exponents from section 6.1 am * an = am+n (am)n = amn (ab)m = ambm 1 -m a = a a a = am-n a a = b m m n m m bm These all work for fraction exponents as well as integer exponents. Ex: 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: Simplify. 3 25 5= a. 3 3 Ex: 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: 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. More Examples x2 x a. b. c. d. 6 x x 11 y11 y 4 6 r8 4 r4 r4 4 r 4 4 r 4 r r r 2 Ex: 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: Write the expression in simplest form. Assume all variables are positive. 4 4 9 a. 12d e f 14 12 d e f 4 4 4 12 d e 4 de 2 f b. 5 34 9 4 24 e f 12ef 4 34 14 f 2 2 2 3 2 3 g2 g h g h 5 5 10 h 7 h7 h3 h 5 g 2 h3 h2 No tents in the basement! 3 2 3 c. 15d e f 3d 4 5df 2 31 3 e f 1( 4 ) 2 2 3 3d e f 5 ** Remember, solutions must be in the same form as the original problem (radical form or rational exponent form)!! 8 d. 4 x y 6 z 11 4 8 11 2 x y z 6 2 z z Can’t have a tent in the basement!! 8 4 11 2 x y z 8 z 2 x y 24 z 3 2 y z 2 Ex: Perform the indicated operation. Assume all variables are positive. a. 8 x 3 x 5 x 1 4 b. 3gh 6 gh 1 4 3gh c. 2 6 x x 4 6 x 4 5 1 4 2x 6x x 6x 4 4 3x 4 6 x d. 6 s 2 s s 6 2 1 s 5 s e. 3 6y 2y 7 3 3y 23 5y 23 6y 2y 23 6y 6y 23 6y