1) $$-9^2 \cdot (-3^2)^3 : 3^8 =$$ 2) $$\frac{25 \cdot (5^4)^3}{125^5} =$$ 3) $$\frac{(-2^5) \cdot (-2^2)^3}{2^9} =$$ 4) $$\frac{2^9}{(-2^5) \cdot (-2^3)^2} =$$ 5) $$\frac{(-7)^4 \cdot 4}{14^3} =$$ 6) Поставь в квадратик верное число $$\frac{a^{\Box} \cdot (a^4)^3}{a^{17}} = \frac{1}{a^2}$$

$$-9^2 \cdot (-3^2)^3 : 3^8 = -81 \cdot (-3^6) : 3^8 = -81 \cdot (-729) : 6561 = 59049 : 6561 = 9$$

$$\frac{25 \cdot (5^4)^3}{125^5} = \frac{5^2 \cdot 5^{12}}{(5^3)^5} = \frac{5^{14}}{5^{15}} = \frac{1}{5}$$

$$\frac{(-2^5) \cdot (-2^2)^3}{2^9} = \frac{-2^5 \cdot (-2^6)}{2^9} = \frac{2^{11}}{2^9} = 2^2 = 4$$

$$\frac{2^9}{(-2^5) \cdot (-2^3)^2} = \frac{2^9}{(-2^5) \cdot 2^6} = \frac{2^9}{-2^{11}} = -\frac{1}{2^2} = -\frac{1}{4}$$

$$\frac{(-7)^4 \cdot 4}{14^3} = \frac{7^4 \cdot 4}{(2 \cdot 7)^3} = \frac{7^4 \cdot 2^2}{2^3 \cdot 7^3} = \frac{7}{2} = 3.5$$

$$\frac{a^{\Box} \cdot (a^4)^3}{a^{17}} = \frac{1}{a^2}$$

$$\frac{a^{\Box} \cdot a^{12}}{a^{17}} = \frac{1}{a^2}$$

$$\frac{a^{\Box + 12}}{a^{17}} = a^{-2}$$

$$a^{\Box + 12 - 17} = a^{-2}$$

$$a^{\Box - 5} = a^{-2}$$

$$\Box - 5 = -2$$

$$\Box = 3$$