Simplify :

$\dfrac{8^{3a} \times 2^5 \times 2^{2a}}{4 \times 2^{11a} \times 2^{-2a}}$

Simplifying the expression :

$\Rightarrow \dfrac{8^{3a} \times 2^5 \times 2^{2a}}{4 \times 2^{11a} \times 2^{-2a}} = \dfrac{(2^3)^{3a} \times 2^5 \times 2^{2a}}{2^2 \times 2^{11a} \times 2^{-2a}} \\[1em] = \dfrac{2^{9a} \times 2^5 \times 2^{2a}}{2^2 \times 2^{11a} \times 2^{-2a}} \\[1em] = \dfrac{2^{9a + 5 + 2a}}{2^{2 + 11a + (-2a)}} \\[1em] = \dfrac{2^{11a + 5}}{2^{9a + 2}} \\[1em] = 2^{(11a + 5) - (9a + 2)} \\[1em] = 2^{11a - 9a + 5 - 2} \\[1em] = 2^{2a + 3}.$

Hence, $\dfrac{8^{3a} \times 2^5 \times 2^{2a}}{4 \times 2^{11a} \times 2^{-2a}} = 2^{2a + 3}$.