\(xy=\dfrac{1}{2};yz=\dfrac{3}{5};xz=\dfrac{27}{16}\)
\(\Rightarrow xy.yz.xz=\dfrac{1}{2}.\dfrac{3}{5}.\dfrac{27}{16}\)
\(\Rightarrow\left(xyz\right)^2=\dfrac{81}{160}\)
\(\Rightarrow\left\{{}\begin{matrix}xyz=\sqrt{\dfrac{81}{160}}\\xyz=-\sqrt{\dfrac{81}{160}}\end{matrix}\right.\)