Given expression: $[∛(x^4 y)×\frac{1}{∜(x^3 y^8 )}]^{-6}$
We start by converting the roots to fractional exponents: $[(x^4 y)^{1/3} × (x^3 y^8 )^{-1/4}]^{-6}$
Then we distribute the exponents to each term inside the brackets: $[x^{4/3} y^{1/3} × x^{-3/4} y^{-2}]^{-6}$
We simplify by adding the exponents of like bases: $[x^{4/3 - 3/4} y^{1/3 - 2}]^{-6} = [x^{7/12} y^{-5/3}]^{-6}$
Finally, we distribute the -6 exponent to get the simplified form: $x^{-7/2} y^{10}$
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