[tex]a) \ \sqrt[3]{5}\cdot\sqrt[3]{25} = \sqrt[3]{5\cdot25} = \sqrt[3]{5\cdot5^{2}} = \sqrt[3]{5^{3}} = 5\\\\b) \ \sqrt[3]{7}\cdot\sqrt[3]{49}=\sqrt[3]{7\cdot49} = \sqrt[3]{7\cdot7^{2}} = \sqrt[3]{7^{3}} = 7\\\\c) \ \sqrt[3]{25}\cdot\sqrt[3]{40} = \sqrt[3]{25\cdot40} = \sqrt[3]{1000} = \sqrt[3]{10^{3}} = 10[/tex]
[tex]d) \ \frac{\sqrt[3]{16}}{\sqrt[3]{2}} = \sqrt[3]{\frac{16}{2}} = \sqrt[3]{8} = \sqrt[3]{2^{3}} = 2\\\\e) \ \frac{\sqrt[3]{81}}{\sqrt[3]{3}} = \sqrt[3]{\frac{81}{3}} = \sqrt[3]{27} = \sqrt[3]{3^{3}} = 3\\\\f) \ \sqrt[3]{40}:\sqrt[3]{5} = \frac{\sqrt[3]{40}}{\sqrt[3]{5}} = \sqrt[3]{\frac{40}{5}} = \sqrt[3]{8} = \sqrt[3]{2^{3}}=2[/tex]
