The simplified form of the expression is [tex]4^{-1/3}[/tex]
Given the indices expression as shown;
[tex]\frac{(4^{1/3}\times 4^{2/6} )^{3/4}}{4^{5/6}}[/tex]
Applying the product and quotient law of indices
[tex]\frac{(4^{1/3+1/3})^{3/4}}{4^{5/6}}\\\frac{(4^{2/3})^{3/4}}{4^{5/6}}\\\frac{4^{1/2}}{4^{5/6}}\\[/tex]
Take the difference in the power to have:
4^(1/2 - 5/6)
4^(-2/6)
[tex]4^{-1/3}[/tex]
Hence the simplified form of the expression is [tex]4^{-1/3}[/tex]
Learn more on indices here: https://brainly.com/question/10339517
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