\[\frac{45xy}{7z^{2}} \cdot \frac{14xz^{3}}{81y^{2}} \cdot \frac{27y^{3}}{5xz} =\]
\[= \frac{45 \cdot 14 \cdot 27 \cdot x^{2}y^{4}z^{3}}{7 \cdot 81 \cdot 5 \cdot xy^{2}z^{3}} = 6xy^{2}\]