Simplify the expressions:

1. Simplify the expressions:

1. \( a^{\frac{3}{11}} \left( a^{\frac{2}{11}} \right)^4 \)

   \( = a^{\frac{3}{11}} \cdot a^{\frac{2}{11} \cdot 4} \)

   \( = a^{\frac{3}{11}} \cdot a^{\frac{8}{11}} \)

   \( = a^{\frac{3}{11} + \frac{8}{11}} \)

   \( = a^{\frac{11}{11}} \)

   \( = a \)

   Ответ: \( a \)

2. \( \frac{\sqrt{ab}}{a + \sqrt{ab}} - \frac{\sqrt{ab} - b}{a - b} \)

   \( = \frac{\sqrt{ab}}{a + \sqrt{ab}} - \frac{\sqrt{b}(\sqrt{a} - \sqrt{b})}{(\sqrt{a} - \sqrt{b})(\sqrt{a} + \sqrt{b})} \)

   \( = \frac{\sqrt{ab}}{a + \sqrt{ab}} - \frac{\sqrt{b}}{\sqrt{a} + \sqrt{b}} \)

   \( = \frac{\sqrt{ab}(\sqrt{a} + \sqrt{b}) - \sqrt{b}(a + \sqrt{ab})}{(a + \sqrt{ab})(\sqrt{a} + \sqrt{b})} \)

   \( = \frac{\sqrt{a^2b} + \sqrt{ab^2} - a\sqrt{b} - \sqrt{ab^2}}{a\sqrt{a} + a\sqrt{b} + \sqrt{a^2b} + \sqrt{ab^2}} \)

   \( = \frac{a\sqrt{b} + b\sqrt{a} - a\sqrt{b} - b\sqrt{a}}{a\sqrt{a} + a\sqrt{b} + a\sqrt{b} + b\sqrt{a}} \)

   \( = \frac{0}{a\sqrt{a} + 2a\sqrt{b} + b\sqrt{a}} = 0 \)

   Ответ: 0

3. \( \frac{y^{0.5}}{y^{0.5} + 4} + \frac{4 \cdot y^{0.5}}{y - 16} \)

   \( = \frac{y^{0.5}}{y^{0.5} + 4} + \frac{4 \cdot y^{0.5}}{(y^{0.5} - 4)(y^{0.5} + 4)} \)

   \( = \frac{y^{0.5}(y^{0.5} - 4) + 4 \cdot y^{0.5}}{(y^{0.5} - 4)(y^{0.5} + 4)} \)

   \( = \frac{y - 4y^{0.5} + 4y^{0.5}}{y - 16} \)

   \( = \frac{y}{y - 16} \)

   Ответ: \( \frac{y}{y - 16} \)

4. \( \sqrt[3]{a} \cdot \sqrt{a} \cdot \sqrt[6]{a^5} \)

   \( = a^{\frac{1}{3}} \cdot a^{\frac{1}{2}} \cdot a^{\frac{5}{6}} \)

   \( = a^{\frac{1}{3} + \frac{1}{2} + \frac{5}{6}} \)

   \( = a^{\frac{2}{6} + \frac{3}{6} + \frac{5}{6}} \)

   \( = a^{\frac{10}{6}} \)

   \( = a^{\frac{5}{3}} \)

   Ответ: \( a^{\frac{5}{3}} \)