Express the following in simplest radical form

Question

(4^(1/2)) (x^(1/6)) (y^(2/3)) 

Answer 1

(4^(1/2)) (x^(1/6)) (y^(2/3)) =

 

2 (x^(1/6)) (y^(4/6)) =

 

2 (x^(1/6)) (y^4)^(1/6) =

 

2 (x y^4)^(1/6)

Answer 2

4^(1/2) * X ^( 1/6) * Y ^( 2/3) =

             

  2 ⁶√x * ³√(y ^ 2)

 

  2 ⁶√X  *  ^3X2√(Y^2) ^2) =                    

 

 

 2 ⁶√ X  * ⁶√Y^4  =

 

  2 ⁶√(X Y^4)  or

 

2 [( XY^4) ^( 1/6)]

 

 

  Note X ^ 1/2 =[ (X ^ 1/2 ) ^ 3 ] ^ 1/3 =[ X^3/2] ^1/3

      

              √2 = 6√(2^3) = ⁶√8

 

   

Answer 3

Hi, Valerie,

 

(4^(1/2)) (x^(1/6)) (y^(2/3))

 

Well, (4^(1/2)) is easy.  That's just 2.

 

Now remember: when you multiply you add the exponents, so

 

(x^(1/6)) (y^(2/3)) = x^((1/6) +(2/3)) = x^((1/6) + (4/6)) = x^(5/6)

 

So

 

(4^(1/2)) (x^(1/6)) (y^(2/3)) = 2x^(5/6) or 2x^(5/6) is the final answer