Hallar el mayor valor de $n$ si:
$$ (n\sqrt{n})^{\frac{1}{\sqrt{n^3}}} = \left[ \left[ \left[ \left[ 2^{(1+\frac{1}{1})} \right]^{(1+\frac{1}{2})} \right]^{(1+\frac{1}{3})} \right]^{(1+\frac{1}{4})} \right]^{\frac{1}{10}} $$
$$ \begin{array}{lllll} \text{(A) } \sqrt[3]{2} & \text{(B) } \sqrt{2} & \text{(C) } 4 & \text{(D) } 3 & \text{(E) } \sqrt[3]{16} \end{array} $$