# Q5SOL - MAP 103 Proficiency Algebra Quiz#5 Fall 2009...

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Unformatted text preview: MAP 103: Proficiency Algebra, Quiz #5, Fall 2009 SOLUTIONS 1. (a) Rewrite with fractional exponents the expression: 3 p 64 x 4 y 2 z 5 . Sol. With fractional exponents, the expression becomes: 3 p 64 x 4 y 2 z 5 = (64 x 4 y 2 z 5 ) 1 / 3 = 64 1 / 3 ( x 4 ) 1 / 3 ( y 2 ) 1 / 3 ( z 5 ) 1 / 3 = (4 3 ) 1 / 3 x 4 / 3 y 2 / 3 z 5 / 3 = 4 x 4 / 3 y 2 / 3 z 5 / 3 (b) Rewrite without fractional exponents the expression: 8 1 / 2 x 2 / 3 y 3 / 2 z 1 / 2 . Sol. Without fractional exponents, the expression becomes: 8 1 / 2 x 2 / 3 y 3 / 2 z 1 / 2 = √ 8 3 √ x 2 p y 3 √ z = √ 4 · 2 3 √ x 2 p y 3 z = √ 4 √ 2 3 √ x 2 p y 3 z = 2 √ 2 3 √ x 2 p y 3 z 2. Solve for x and check: √ x + 5 = x + 3 . Sol. We first solve for x. √ x + 5 = x + 3 ( √ x + 5) 2 = ( x + 3) 2 x + 5 = ( x + 3)( x + 3) x + 5 = x 2 + 6 x + 9 0 = x 2 + 6 x + 9- x- 5 0 = x 2 + 5 x + 4 0 = ( x + 1)( x + 4) It follows x =- 1 ,- 4 ....
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Q5SOL - MAP 103 Proficiency Algebra Quiz#5 Fall 2009...

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