$8sqrt 8 imes {8^3} div {8^{ - frac{{15}}{2}}} = {2^?}$

$frac{{8sqrt 8 imes {8^3}}}{{{8^{ - frac{{15}}{2}}}}} = {2^?}$

$Rightarrow 8sqrt 8 imes {8^3} imes {8^{frac{{15}}{2}}} = {2^2}$

$Rightarrow {(8)^{frac{3}{2} + 3 + frac{{15}}{2}}} = {2^?}$

$Rightarrow {(8)^{frac{{3 + 6 + 15}}{2}}} = {2^?}$

$Rightarrow {8^{12}} = {2^?} Rightarrow {(2)^{36}} = {2^?}$

$Rightarrow ? = 36$