Cho \(a>0\). Biết \(\sqrt[3]{{a\sqrt[3]{{a\sqrt[3]{{a\sqrt[3]{a}}}}}}} = {a^x}\). Tìm \(x\).

A. \(x = \frac{4}{9}\)

B. \(x = \frac{1}{{81}}\)

C. \(x = \frac{{40}}{{81}}\)

D. \(x = \frac{{13}}{{27}}\)