Evaluating Indices: Fractions, Roots, and Powers

Evaluate each of the following without the use of a calculator.

1. \({{27}^{\frac{2}{3}}}\)
2. \({{16}^{1.5}}\)
3. \({{27}^{\frac{1}{3}}}\times {{3}^{-1}}\)
4. \({{\left( \frac{3}{4} \right)}^{-2}}\div {{16}^{-\frac{1}{2}}}\)
5. \({{8}^{-\frac{2}{3}}}\times {{\left( \frac{2}{5} \right)}^{2}}\div {{5}^{-2}}\)
6. \({{\left( \frac{1}{4} \right)}^{0}}-\sqrt{64}+{{\left( \frac{1}{2} \right)}^{-3}}\)