If $\log_6 x + 2\log_{36} x + 3\log_{216} x = 9$, then $x =$ ___

Since $36 = 6^2$ and $216 = 6^3$, all bases can be converted to base 6 using the property $\log_{a^n} x = \dfrac{1}{n}\log_a x$

$2\log_{36} x = 2 \cdot \log_{6^2} x = 2 \cdot \dfrac{\log_6 x}{2} = \log_6 x$

$3\log_{216} x = 3 \cdot \log_{6^3} x = 3 \cdot \dfrac{\log_6 x}{3} = \log_6 x$

Substituting back into the original equation:

$\log_6 x + \log_6 x + \log_6 x = 9$

$3\log_6 x = 9$

$\log_6 x = 3$

$x = 6^3 = \boxed{216}$