# Past, present, and everything in between

**Algebra**Level 5

\[ \Large \prod_{i=1}^{2^{2015}} \left( \sqrt[2^i]{2015} + \sqrt[2^i]{1995} \right) \]

Given that the reciprocal of the product above can be expressed as \(\large \dfrac 1d \left( a^{1/2^b} - c^{1/2^b} \right) \) where \(a,b,c\) and \(d\) are positive integers. What is the value of \(\large \dfrac{c \log_2( b) + 5a}{\log_2 (b^d)}? \)