Question 3
Given that $x$, $y$, and $z$ are positive real numbers such that
$$x^{\log_{2}(yz)} = 2^{8} \cdot 3^{4}, \quad y^{\log_{2}(zx)} = 2^{9} \cdot 3^{6}, \quad \text{and} \quad z^{\log_{2}(xy)} = 2^{5} \cdot 3^{10},$$
compute the smallest possible value of $xyz$.
$$x^{\log_{2}(yz)} = 2^{8} \cdot 3^{4}, \quad y^{\log_{2}(zx)} = 2^{9} \cdot 3^{6}, \quad \text{and} \quad z^{\log_{2}(xy)} = 2^{5} \cdot 3^{10},$$
compute the smallest possible value of $xyz$.