Note that $2^10=1024$ so $2^{2002}=(2^{10})^{200}\cdot 4$. Clearly, $(2^{10})^{200}\ll 2000^{200}$. Thus, a factor of $4$ has virtually no value so the answer is $2000^{200}$.

$2000^{200}>1.95^{200}\cdot1024^{200}>2^{2002}$