[tex]1) \ 25^{-\frac{3}{2}} = (5^{2})^{-\frac{3}{2}} = 5^{2\cdot(-\frac{3}{2})} = 5^{-3} = (\frac{1}{5})^{3} = \frac{1}{125}\\\\\\3) \ \frac{3\sqrt{7}-2}{\sqrt{7}} = \frac{3\sqrt{7}-2}{\sqrt{7}}\cdot\frac{\sqrt{7}}{\sqrt{7}} = \frac{3\cdot7-2\sqrt{7}}{7} =\frac{21-2\sqrt{7}}{7}\\\\\\4) \ log_{\frac{1}{3}}\sqrt[4]{9} = log_{\frac{1}{3}}((\frac{1}{3})^{-2})^{4} = log_{\frac{1}{3}}(\frac{1}{3})^{-8} = -8[/tex]
[tex]5) \ \sqrt{125}-\sqrt{80}+3\sqrt{20} = \sqrt{25\cdot5}-\sqrt{16\cdot5}+3\sqrt{4\cdot5} =\\\\= \sqrt{25}\cdot\sqrt{5}-\sqrt{16}\cdot\sqrt{5}+3\cdot\sqrt{4}\cdot\sqrt{5}=5\sqrt{5}-4\sqrt{5}+3\cdot2\sqrt{5} = \sqrt{5}+6\sqrt{5} = 7\sqrt{5}[/tex]
