Radicals are Fun!!!

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 \( \sqrt [ 5 ]{ { x }^{ 4 }(\sqrt [ 4 ]{ { x }^{ 3 }(\sqrt [ 3 ]{ { x }^{ 2 }(\sqrt { x } } } } \).


This problem is original.
×

Problem Loading...

Note Loading...

Set Loading...