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Simplify \(^{x\sqrt{y}}/_{y\sqrt{x}}\) if \(x>0\) and \(y>0\).

 

A. \(^{\sqrt{y}}/_{xy}\)

B. \(^{\sqrt{y}}/_y\)

C. \(^{\sqrt{xy}}/_y\)

D. \(^{x\sqrt{xy}}/_y\)

 

P.S. this is different than Plato Classroom Question #13; it has variables instead of numbers and variables.

 Jan 23, 2018
 #1
avatar+101085 
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[ x √y ]  / [ y √ x ]

 

Write in exponential form

 

[ x * y^1/2 ] / [ y * x^1/2 ]       and we can write

 

[ x^1 / x^1/2 ]  *  [ y^1/2  / y^1  ]

 

Remember that        a^m / a^n   =   a^( m - n)

 

So we have

 

x^(1 - 1/2)  *  y^(1/2  - 1)

 

x^1/2   *   y^(-1/2) =

 

√x / √y          multiply top/bottom by √y

 

[ √ x√ y ]  / y

 

√[ xy] / y  ⇒   "C"

 

 

 

cool cool cool

 Jan 23, 2018

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