# Section_1.2-Exponents_and_Radicals - Section 1.2 Exponents...

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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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