If $N > 1$, then $\sqrt[3]{N\sqrt[3]{N\sqrt[3]{N}}} =$
$\mathrm{(A) \ } N^{\frac 1{27}} \qquad \mathrm{(B) \ } N^{\frac 1{9}} \qquad \mathrm{(C) \ } N^{\frac 1{3}} \qquad \mathrm{(D) \ } N^{\frac {13}{27}} \qquad \mathrm{(E) \ } N$
The key identities are $\sqrt[3]{x^n} = x^{\frac{n}{3}}$ and $x \cdot x^{\frac{a}{b}} = x^{1 + \frac{a}{b}}$
$\sqrt[3]{N\sqrt[3]{N\sqrt[3]{N}}}$
$\sqrt[3]{N\sqrt[3]{N\cdot N^{\frac{1}{3}}}}$
$\sqrt[3]{N\sqrt[3]{N^{\frac{4}{3}}}}$
$\sqrt[3]{N\cdot{N^{\frac{4}{9}}}}$
$\sqrt[3]{{N^{\frac{13}{9}}}}$
$N^{\frac{13}{27}}$, thus the answer is $\boxed{D}$