Algebra Level 4

$\sqrt[n]{x^{n-1} \big ( \sqrt[n-1]{ x^{n-2} \big ( \sqrt[n-2]{x^{n-3} \cdots \sqrt x } }}$

Consider the nested expression above. When $$n=12345678987654321$$, the expression can be simplified to $$x^{1- 1/a!}$$.

Compute $$\dfrac a{100}$$.

For instance, for $$n=5$$, the expression is in the form $$\sqrt [ 5 ]{ { x }^{ 4 }(\sqrt [ 4 ]{ { x }^{ 3 }(\sqrt [ 3 ]{ { x }^{ 2 }(\sqrt { x } } } }$$.

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