IKMC 2010 - Grades 11-12 - Paper 02 - Self-study Question 27

Let $P=(2+3)(2^2+3^2)\cdots$
$\cdots(2^{1024}+3^{1024})(2^{2048}+3^{2048})$.
Evaluate $\dfrac{P+2^{4096}}{3^{2048}}$. The product exponents double each time.