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What is the simplest radical form of the expression?

(x^4y^7)^2/3

 

Options: 

xy^2 3Sqrt x y

x^6y^10 Sqrt y

x^2y^4 3Sqrt x^2y^2

x^3y^5 Sqrtx

 

My answer-'D' Am I correct?

 Jan 16, 2018
 #1
avatar+101760 
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(x^4y^7)^2/3  =

 

 ( [ x^4 y^7] ^2 ) ^1/3   =

 

( x^8 y^14 ) ^1/3  =

 

∛  [  x^8  y^14 ]  =

 

To determine  the powers that come out and those that stay in, do this

 

8/3  =   2  + 2/3          2 powers of x come out, 2 stay in

14/3  =  4  + 2/3         4 powers of x come out, 2 stay  in

 

x^2 y ^4  ∛  [x^2  y ^2 ]   

 

 

cool cool cool     .

 Jan 16, 2018

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