x4 x3 x2 x345=x4 x3 x2 x1/2345=x4 x3 x5/2345=x4 x3 x5/645=x4 x3 x5/645=x4 x23/645=x4 x23/245=x119/245=x119/120

simplify:

\sqrt[5]{x^{4} . \sqrt[4]{x^{3} . \sqrt[3]{x^{2} . \sqrt{x}}}} = \sqrt[5]{x^{4} . \sqrt[4]{x^{3} . \sqrt[3]{x^{2} . x^{1 / 2}}}} = \sqrt[5]{x^{4} . \sqrt[4]{x^{3} . \sqrt[3]{x^{5 / 2}}}} = \sqrt[5]{x^{4} . \sqrt[4]{x^{3} . x^{5 / 6}}} = \sqrt[5]{x^{4} . \sqrt[4]{x^{3} . x^{5 / 6}}} = \sqrt[5]{x^{4} . \sqrt[4]{x^{23 / 6}}} = \sqrt[5]{x^{4} . x^{23 / 24}} = \sqrt[5]{x^{119 / 24}} = x^{119 / 120}