jmc

Using the associative property and simplifying gives $$\begin{array}{rl}(15x^2)\cdot (6x)\cdot \left(\frac{1}{(3x{)}^2}\right)& =(15\cdot 6)\cdot (x^2\cdot x)\cdot \left(\frac{1}{9x^2}\right)\\ & =\frac{90x^3}{9x^2}\\ & =10x^{3-2}=\boxed{10x}.\end{array}$$