[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\\\\\\d)\ \ \frac{\sqrt[3]{16}}{\sqrt[3]{2}}=\sqrt[3]{\frac{16}{2}}=\sqrt[3]{8}=2[/tex]
[tex]e)\ \ \frac{\sqrt[3]{81}}{\sqrt[3]{3}}=\sqrt[3]{\frac{81}{3}}=\sqrt[3]{27}=3\\\\\\f)\ \ \sqrt[3]{40}:\sqrt[3]{5}=\frac{\sqrt[3]{40}}{\sqrt[3]{5}}=\sqrt[3]{\frac{40}{5}}=\sqrt[3]{8}=2[/tex]
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[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\\\\\\d)\ \ \frac{\sqrt[3]{16}}{\sqrt[3]{2}}=\sqrt[3]{\frac{16}{2}}=\sqrt[3]{8}=2[/tex]
[tex]e)\ \ \frac{\sqrt[3]{81}}{\sqrt[3]{3}}=\sqrt[3]{\frac{81}{3}}=\sqrt[3]{27}=3\\\\\\f)\ \ \sqrt[3]{40}:\sqrt[3]{5}=\frac{\sqrt[3]{40}}{\sqrt[3]{5}}=\sqrt[3]{\frac{40}{5}}=\sqrt[3]{8}=2[/tex]