1) \( \frac{2}{\left(2^{2}\right)^{3} \cdot 2^{4}} \)

To simplify \( \frac{2}{\left(2^{2}\right)^{3} \cdot 2^{4}} \), we can start by simplifying the expression in the denominator. Recall that \( \left(2^{2}\right)^{3} = 2^{2 \cdot 3} = 2^{6} \). Thus, we rewrite the denominator: \[ \left(2^{2}\right)^{3} \cdot 2^{4} = 2^{6} \cdot 2^{4} = 2^{6 + 4} = 2^{10}. \] Now we can substitute this back into the original expression: \[ \frac{2}{2^{10}}. \] We know that \( 2 = 2^{1} \), so we can rewrite it as: \[ \frac{2^{1}}{2^{10}} = 2^{1 - 10} = 2^{-9}. \] Therefore, the simplified result is \( 2^{-9} \) which is equivalent to \( \frac{1}{2^{9}} \).