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mac1140_lecture2_2 - L2 1.3 Polynomials Binomial Theorem...

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11 L2 §1.3 Polynomials; Binomial Theorem Rules for Exponents Product Rule : For all positive integers , m n and every real number a : m n m n a a a + = Example . Find the following products: 6 3 z z = 2 12 2 3 (2 ) (2 ) x x π π + + = 3 7 4 (7 )(2 ) x y x y = Definition : For any nonzero real number a , 0 1 a = Note : expression 0 0 is undefined. Example . Evaluate each power: 0 ( 7) = vs. 0 7 = 0 2 2( 3) − − + = 12 Power Rules : For all positive integers m and n and all real a and b , ( ) m n mn a a = ( ) m m m ab a b = ( ) 0 m m m a a b b b = Example . Simplify: 7 2 2 ( ) b c = 3 2 3 2 2 ( ) x z x z = 5 2 4 0 3 x y z w = Caution! 3 ab vs. ( ) 3 ab 2 ( ) a b + vs. 2 2 a b +
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