Advanced Simplification with Index Laws

Simplify each of the following

1. \({{a}^{7}}\times {{a}^{3}}\div {{\left( {{a}^{3}} \right)}^{2}}\)
2. \({{\left( 2b \right)}^{5}}\div 8{{b}^{2}}\)
3. \({{\left( \frac{3{{x}^{2}}}{{{x}^{3}}} \right)}^{3}}\div \frac{27{{x}^{7}}}{{{x}^{21}}}\)
4. \({{\left( {{c}^{2}}d \right)}^{4}}\times {{\left( {{c}^{4}}{{d}^{3}} \right)}^{5}}\)
5. \(5{{\left( ef \right)}^{3}}\times 10e{{f}^{2}}\)
6. \(16{{m}^{8}}{{n}^{7}}\div {{\left( -2{{m}^{3}}{{n}^{2}} \right)}^{2}}\)
7. \({{\left( \frac{{{p}^{2}}}{q} \right)}^{6}}\times {{\left( \frac{2{{q}^{2}}}{-3{{p}^{5}}} \right)}^{3}}\)