Question 981108
If you mean:
{{{sqrt(2xy^2)/root(3,8xy^3)}}}
= {{{y*sqrt(2x)/(2y*root(3,x))}}}
= {{{sqrt(2x)*root(3,x^2)/(2root(3,x)*root(3,x^2))}}}
= {{{sqrt(2x)*root(3,x^2)/(2*root(3,x^3))}}}
= {{{sqrt(2x)*root(3,x^2)/2x}}}
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= {{{root(6,(2x)^3)*root(6,(x^2)^2)/2x}}}
= {{{root(6,8x^7)/2x}}}
= {{{x*root(6,8x)/2x}}}
= {{{root(6,8x)/2}}}
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Your use of parentheses doesn't eliminate the ambiguities.