а) 4³ · 3¹⁰ / 6¹⁰; 6) 2⁶ · 6¹⁸ / 2²⁵ · 9⁹

• а) $$ \frac{4^3 \cdot 3^{10}}{6^{10}} = \frac{(2^2)^3 \cdot 3^{10}}{(2 \cdot 3)^{10}} = \frac{2^6 \cdot 3^{10}}{2^{10} \cdot 3^{10}} = \frac{2^6}{2^{10}} = 2^{6-10} = 2^{-4} = \frac{1}{2^4} = \frac{1}{16} $$
• б) $$ \frac{2^6 \cdot 6^{18}}{2^{25} \cdot 9^9} = \frac{2^6 \cdot (2 \cdot 3)^{18}}{2^{25} \cdot (3^2)^9} = \frac{2^6 \cdot 2^{18} \cdot 3^{18}}{2^{25} \cdot 3^{18}} = \frac{2^{6+18} \cdot 3^{18}}{2^{25} \cdot 3^{18}} = \frac{2^{24} \cdot 3^{18}}{2^{25} \cdot 3^{18}} = \frac{2^{24}}{2^{25}} = 2^{24-25} = 2^{-1} = \frac{1}{2} $$

Ответ: а) 1/16; б) 1/2