Упрощение с помощью корней: 1) \(3^{1/2}\); 2) \(2^{-3/2}\); 3) \(5^{2/3}\); 4) \(3^{-6/5}\); 5) \(5^{9,5}\); 6) \(2^{1/2}\cdot5^{1/5}\).

Используем правила \(a^{m/n}=\sqrt[n]{a^m}\) и \(a^{-r}=1/a^r\).

1. \(3^{1/2}=\sqrt3.\)
2. \(2^{-3/2}=1/2^{3/2}=1/(2\sqrt2)=\sqrt2/4.\)
3. \(5^{2/3}=\sqrt[3]{25}.\)
4. \(3^{-6/5}=1/3^{6/5}=1/(3\sqrt[5]{3}).\)
5. \(5^{9,5}=5^{19/2}=5^9\sqrt5.\)
6. \(2^{1/2}\cdot5^{1/5}=\sqrt2\cdot\sqrt[5]{5}.\)

Ответ: \(\sqrt3\); \(\frac{\sqrt2}{4}\); \(\sqrt[3]{25}\); \(\frac{1}{3\sqrt[5]{3}}\); \(5^9\sqrt5\); \(\sqrt2\cdot\sqrt[5]{5}\).