Math 017 Materials With Exercises

Solution:626 2 6 6 6 266 12 6 12a) b)( x)(y ) ( 1x)( y ) ( 1)x y 1xy x y2 4ab2 ab32 (4a21b32)21 (4ab1)2 (4ab)22 4 a2b22 16ab2(3xExample 4.8 Simplify the expression3 4x x5 ) 21and then evaluate, when x .2Solution:5 2 2 5 2 5210(3x) 3 ( x ) 9x9x 9x3 4347 7x x x x x1To evaluate, we substitute x .23107 9x33 1 1( 1) 19x 9 9 9 9 . 2 2 2 8 89333Example 4.9 Which of the following expressions are equivalent to4 x7 2y ,( 2 y2 7x ) ,4 y2 5 2x ( ) , xy 7 x4 ,4 y2 7x ?2 3 44xy ySolution:2 5 2 2 5224x( y ) 4xy 4xy10, and hence2 54x( y7 2equivalent. 4yx is equivalent because only the order of factorschanged.2 7 2 2 7 2 7( 2x)y 2 x y 4xy ,77 2 74xyx 4xxy 4xy ,2 3 4 2 342 74xy y 4xy 4xy.)2is not equivalent. All others are7y andExample 4.10 Find the numerical value of such that the following statements are true.a) 4 6 3 7 2b) 36 6 62x has beenSolution:6a) We must express 4 as an exponential expression with the base 2 (to match it26 2 6 12to 2 ). Since 4 2 , we get 4 (2 ) 2 . As a result 2 12 2 , hence 12.b) We must express2Notice that 36 6 , and thus3 736 6 as an exponential expression with the base 6.3 7 2 3 7 6 7 1336 6 (6 ) 6 6 6 6 ; 13.819Example 4.11 Evaluate. a)8097 64 4b)114Solution:43