Simplifying Complex Expressions with Rational Indices

Simplify each of the following, expressing your answers in positive index notation.

1. \(\sqrt[3]{a}\times 5{{a}^{\frac{5}{3}}}\)
2. \({{\left( \sqrt{m} \right)}^{3}}\times {{\left( \sqrt[3]{m} \right)}^{4}}\div {{\left( \sqrt[6]{m} \right)}^{5}}\)
3. \(2{{x}^{2}}\times {{\left( \frac{25{{x}^{2}}}{4{{y}^{4}}} \right)}^{\frac{1}{2}}}\)
4. \(\frac{{{p}^{2}}}{2{{q}^{4}}}\div \frac{\sqrt{p}}{{{(4{{q}^{3}})}^{2}}}\)
5. \({{\left( -3{{m}^{2}}{{n}^{-\frac{2}{3}}} \right)}^{3}}\times \sqrt[3]{8mn}\)