# Exponential product

Calculus Level 3

$P=\prod _{ n=1 }^{ \infty }{ \left[ \prod _{ m=1 }^{ 4 }{ { \left( \frac { 2000 }{ { 2 }^{ m } } \right) }^{ \frac { 1 }{ { n }^{ 2 } } } } \right] }$

If $$P$$ can be expressed in the form $${ A }^{ { \pi }^{ B } }$$, where $$A$$ and $$B$$ are positive integers, find the value of $$\frac { A }{ B }$$.

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