Question 487734
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How would you put this into radical form: (8x)2/3.
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The solution and the answer  {{{root(3,x^2)}}}  in the post by @Theo both are incorrect.


The correct answer is    {{{4*root(3,x^2)}}}.



Indeed,  you can consider  (8x)^(2/3)  as the square of the cube root of  (8x)^(1/3).


Doing this way, you will get   {{{(root(3,8x))^2}}} = {{{(2*root(3,x))^2}}} = {{{4*root(3,x^2)}}}.



Alternatively,  you can consider   (8x)^(2/3)  as the cube root of  (8x)^2 = 64x^2.


Doing this way,  you will get   {{{root(3,64x^2)}}} = {{{4*root(3,x^2)}}}.



Thus,  either way leads to the same answer   {{{4*root(3,x^2)}}}.



Solved correctly.