mac1140_lecture5_1

mac1140_lecture5_1 - L5 1.6 Rational Exponents Negative...

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36 L5 §1.6 Rational Exponents Negative exponents : For all real 0 a and integers n , 1 n n a a = . In particular, 1 1 a a = . Example . Write without negative exponents and simplify. a) 2 5 b) 2 32 c) 24 xy Caution. A negative exponent indicates a reciprocal , not a negative expression. Thus, if 0 a and 0 b , then nn ab ba ⎛⎞ = ⎜⎟ ⎝⎠ .
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37 Example . Simplify each expression. a) 3 2 3 ⎛⎞ ⎜⎟ ⎝⎠ b) 2 1 3 3 x y Quotient Rule: For all integers m , n and all real 0 a , m mn n a a a = . Indeed, m n a a = Example . Simplify: a) 7 3 4 4 b) 8 5 (5 ) )
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38 c) 23 31 x y x y −− Note : in part (c) above we could have rewritten the expression using positive exponents before applying the Quotient Rule. 1 n a = Since 1 n n a a = and 1 n n a a = , the following is true: If the expression is a factor , we can move the expression from the numerator to denominator or otherwise by changing the sign on the exponent.
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This note was uploaded on 02/29/2012 for the course MAC 1140 taught by Professor Gregory during the Fall '11 term at Broward College.

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mac1140_lecture5_1 - L5 1.6 Rational Exponents Negative...

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