64. Найдите значение выражения: 1) 2⁹ · 3⁹ / 6⁷; 2) 18⁷ / 2⁶ · 9⁶; 3) 7⁹ · 5⁸ / 35⁸; 4) 2⁹ · 5¹⁴ / 50⁷; 5) 100⁸ / 2¹⁵ · 5¹⁴; 6) 45⁴ / 75³.

1. $$\frac{2^9 \cdot 3^9}{6^7} = \frac{(2 \cdot 3)^9}{6^7} = \frac{6^9}{6^7} = 6^{9-7} = 6^2 = 36$$
2. $$\frac{18^7}{2^6 \cdot 9^6} = \frac{18^7}{2^6 \cdot (9^1)^6} = \frac{18^7}{(2 \cdot 9)^6} = \frac{18^7}{18^6} = 18^{7-6} = 18$$
3. $$\frac{7^9 \cdot 5^8}{35^8} = \frac{7^9 \cdot 5^8}{(7 \cdot 5)^8} = \frac{7^9 \cdot 5^8}{7^8 \cdot 5^8} = \frac{7^9}{7^8} = 7$$
4. $$\frac{2^9 \cdot 5^{14}}{50^7} = \frac{2^9 \cdot 5^{14}}{(2 \cdot 25)^7} = \frac{2^9 \cdot 5^{14}}{(2 \cdot 5^2)^7} = \frac{2^9 \cdot 5^{14}}{2^7 \cdot 5^{14}} = \frac{2^9}{2^7} = 2^2 = 4$$
5. $$\frac{100^8}{2^{15} \cdot 5^{14}} = \frac{(4 \cdot 25)^8}{2^{15} \cdot 5^{14}} = \frac{(2^2 \cdot 5^2)^8}{2^{15} \cdot 5^{14}} = \frac{2^{16} \cdot 5^{16}}{2^{15} \cdot 5^{14}} = 2 \cdot 5^2 = 50$$
6. $$\frac{45^4}{75^3} = \frac{(3^2 \cdot 5)^4}{(3 \cdot 5^2)^3} = \frac{3^8 \cdot 5^4}{3^3 \cdot 5^6} = \frac{3^5}{5^2} = \frac{243}{25}$$

Ответ:

1. $$36$$
2. $$18$$
3. $$7$$
4. $$4$$
5. $$50$$
6. $$\frac{243}{25}$$