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Unformatted text preview: Section 1.2 Exponents and Radicals Integer Exponents A product of identical numbers is usually written in exponential notation. For example, 5 5 5 is written as 5 3 . In general, we have the following definition. EXAMPLES: (a) ( 1 2 ) 5 = ( 1 2 )( 1 2 )( 1 2 )( 1 2 )( 1 2 ) = 1 32 (b) ( 3) 4 = ( 3) ( 3) ( 3) ( 3) = 81 (c) 3 4 = (3 3 3 3) = 81 EXAMPLES: (a) ( 4 7 ) = 1 , ( + a 3 + b c 2 + d 4 + 2 ) = 1 (b) 0 is undefined (c) x 1 = 1 x 1 = 1 x (d) ( 2) 3 = 1 ( 2) 3 = 1 8 = 1 8 (e) 2 3 = 1 2 3 = 1 8 1 Rules for Working with Exponents In the table the bases a and b are real numbers, and the exponents m and n are integers. EXAMPLES: (a) x 4 x 7 (1) = x 4+7 = x 11 (b) y 4 y 7 (1) = y 4+( 7) = y 3 = 1 y 3 (c) c 9 c 5 (2) = c 9 5 = c 4 (d) ( b 4 ) 5 (3) = b ( 4) ( 5) = b 20 (e) (3 x ) 3 (4) = 3 3 x 3 = 27 x 3 (f) ( x 2 ) 5 (5) = x 5 2 5 = x 5 32 EXAMPLES: Simplify (a) (2 a 3 b 2 )(3 ab 4 ) 3 (b) ( x y ) 3 ( y 2 x z ) 4 Solution: (a) (2...
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This note was uploaded on 01/23/2012 for the course MATH 8650 taught by Professor Kiryltsishchanka during the Spring '12 term at NYU.
 Spring '12
 KIRYLTSISHCHANKA
 Calculus, Algebra, Radicals, Exponents

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