\[\boxed{\text{466\ (466).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ \frac{4^{3} \cdot 3^{10}}{6^{10}} = \frac{\left( 2^{2} \right)^{3} \cdot 3^{10}}{2^{10} \cdot 3^{10}} = \frac{2^{6}}{2^{10}} =\]
\[= \frac{1}{2^{10 - 6}} = \frac{1}{2^{4}} = \frac{1}{16}\]
\[\textbf{б)}\ \frac{2^{6} \cdot 6^{18}}{2^{25} \cdot 9^{9}} = \frac{2^{6} \cdot 2^{18} \cdot 3^{18}}{2^{25} \cdot \left( 3^{2} \right)^{9}} =\]
\[= \frac{2^{24} \cdot 3^{18}}{2^{25} \cdot 3^{18}} = \frac{1}{2}\]