Вычислите значения выражений, представленных в таблице.

Для решения представленных выражений, воспользуемся свойствами степеней и корней.

Строка 6:

* $$\frac{1}{16^4} = \frac{1}{(2^4)^4} = \frac{1}{2^{16}} = 2^{-16}$$
* $$\frac{1}{64^2} = \frac{1}{(2^6)^2} = \frac{1}{2^{12}} = 2^{-12}$$
* $$\frac{1}{8^3} = \frac{1}{(2^3)^3} = \frac{1}{2^9} = 2^{-9}$$
* $$\frac{1}{32^5} = \frac{1}{(2^5)^5} = \frac{1}{2^{25}} = 2^{-25}$$
* $$\frac{1}{27^3} = \frac{1}{(3^3)^3} = \frac{1}{3^9} = 3^{-9}$$
* $$\frac{1}{81^4} = \frac{1}{(3^4)^4} = \frac{1}{3^{16}} = 3^{-16}$$
* $$\frac{1}{64^3} = \frac{1}{(2^6)^3} = \frac{1}{2^{18}} = 2^{-18}$$
* $$\frac{1}{25^2} = \frac{1}{(5^2)^2} = \frac{1}{5^4} = 5^{-4}$$

Строка 7:

* $$\frac{1}{32^5} = \frac{1}{(2^5)^5} = \frac{1}{2^{25}} = 2^{-25}$$
* $$\frac{1}{9^2} = \frac{1}{(3^2)^2} = \frac{1}{3^4} = 3^{-4}$$
* $$\frac{1}{125^3} = \frac{1}{(5^3)^3} = \frac{1}{5^9} = 5^{-9}$$
* $$\frac{1}{8^3} = \frac{1}{(2^3)^3} = \frac{1}{2^9} = 2^{-9}$$
* $$\frac{1}{16^4} = \frac{1}{(2^4)^4} = \frac{1}{2^{16}} = 2^{-16}$$
* $$\frac{1}{81^4} = \frac{1}{(3^4)^4} = \frac{1}{3^{16}} = 3^{-16}$$
* $$(\frac{1}{27})^3 = (\frac{1}{3^3})^3 = (3^{-3})^3 = 3^{-9}$$

Строка 8:

* $$(\sqrt[2]{32})^5 = (\sqrt[2]{2^5})^5 = (2^{\frac{5}{2}})^5 = 2^{\frac{25}{2}}$$
* $$4^2 = 16$$
* $$\frac{1}{64^6} = \frac{1}{(2^6)^6} = \frac{1}{2^{36}} = 2^{-36}$$
* $$\frac{1}{32^5} = \frac{1}{(2^5)^5} = \frac{1}{2^{25}} = 2^{-25}$$
* $$(\sqrt[2]{27})^3 = (\sqrt[2]{3^3})^3 = (3^{\frac{3}{2}})^3 = 3^{\frac{9}{2}}$$
* $$\frac{1}{16^4} = \frac{1}{(2^4)^4} = \frac{1}{2^{16}} = 2^{-16}$$
* $$(\sqrt[3]{8})^3 = (2)^3 = 8$$