\frac{25^{\frac{1}{2}}*\sqrt5*\sqrt[6]5}{5^{\frac{2}{3}}}=\frac{(5^2)^{\frac{1}{2}}*5^{\frac{1}{2}}*5^{\frac{1}{6}}}{5^{\frac{2}{3}}}=\frac{5^{1+\frac{1}{2}+\frac{1}{6}}}{5^{\frac{2}{3}}}=
\frac{5^{\frac{3}{2}+\frac{1}{6}}}{5^{\frac{2}{3}}}=\frac{5^{\frac{10}{6}}}{5^{\frac{4}{6}}}=5^{\frac{6}{6}}=5
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\frac{2^{-2}}{\sqrt{2^3}}=\frac{2^{-2}}{2^{\frac{3}{2}}}=2^{-2-\frac{3}{2}}=2^{-3\frac{1}{2}}=2^{-\frac{7}{2}}