Решение:

a) $$\sqrt[4]{16 \cdot 81} = \sqrt[4]{2^4 \cdot 3^4} = \sqrt[4]{(2 \cdot 3)^4} = 2 \cdot 3 = 6$$

в) $$\sqrt[5]{0,00032 \cdot 5^{10}} = \sqrt[5]{\frac{32}{100000} \cdot 5^{10}} = \sqrt[5]{\frac{2^5}{10^5} \cdot 5^{10}} = \sqrt[5]{\frac{2^5}{2^5 \cdot 5^5} \cdot 5^{10}} = \sqrt[5]{5^5} = 5$$

д) $$\sqrt[4]{\frac{7^8}{0,0625}} = \sqrt[4]{\frac{7^8}{\frac{625}{10000}}} = \sqrt[4]{\frac{7^8}{\frac{5^4}{10^4}}} = \sqrt[4]{\frac{7^8 \cdot 10^4}{5^4}} = \sqrt[4]{\frac{7^8 \cdot 2^4 \cdot 5^4}{5^4}} = \sqrt[4]{7^8 \cdot 2^4} = \sqrt[4]{(7^2)^4 \cdot 2^4} = 7^2 \cdot 2 = 49 \cdot 2 = 98$$

б) $$\sqrt[3]{2^6 \cdot 5^3} = \sqrt[3]{2^{3 \cdot 2} \cdot 5^3} = \sqrt[3]{(2^2)^3 \cdot 5^3} = \sqrt[3]{4^3 \cdot 5^3} = \sqrt[3]{(4 \cdot 5)^3} = 4 \cdot 5 = 20$$

г) $$\sqrt[6]{\frac{3^6}{5^{12}}} = \sqrt[6]{\frac{3^6}{(5^2)^6}} = \sqrt[6]{\frac{3^6}{25^6}} = \frac{3}{25} = 0,12$$

е) $$\sqrt{\frac{2^7 \cdot 3^{21}}{5^{14}}} = \sqrt{\frac{2 \cdot 2^6 \cdot 3 \cdot 3^{20}}{(5^7)^2}} = \sqrt{\frac{2 \cdot (2^3)^2 \cdot 3 \cdot (3^{10})^2}{(5^7)^2}} = \sqrt{\frac{2 \cdot 8^2 \cdot 3 \cdot (3^{10})^2}{(5^7)^2}} = \frac{\sqrt{6} \cdot 3^{10}}{5^7} = \frac{\sqrt{6} \cdot 59049}{78125} \approx 1,829 \cdot \sqrt{6}$$

Ответ:

a) 6

в) 5

д) 98

б) 20

г) 0,12

е) $$\frac{\sqrt{6} \cdot 59049}{78125}$$