\(\small{{1.000.000^{{\textstyle{2 \over 3}}}} = {10^{6 \cdot {\textstyle{2 \over 3}}}} = {10^4} = 10.000}\)
\(\small{{1.000.000^{ \text- {\textstyle{2 \over 3}}}} = {10^{6 \cdot\text - {\textstyle{2 \over 3}}}} = {10^{\text - 4}} = \frac{1}{{10.000}}}\)
\(\small{{1000^{ \text- 1{\textstyle{1 \over 3}}}} = {10^{3 \cdot \text - {\textstyle{4 \over 3}}}} = {10^{\text - 4}} = \frac{1}{{10.000}}}\)
\(\small{{1.000.000^{ \text- {\textstyle{2 \over 3}}}} \cdot {1.000.000^{{\textstyle{5 \over 6}}}} = {1.000.000^{{\textstyle{5 \over 6}-{2\over3}} }} = {10^{6 \cdot {\textstyle{1 \over 6}}}} = 10}\)
\(\small{\frac{{{6^{{\textstyle{1 \over 2}}}}}}{{{6^{1{\textstyle{1 \over 2}}}}}} = {6^{{\textstyle{1 \over 2}} - 1{\textstyle{1 \over 2}}}} = {6^{ \text- 1}} = {\textstyle{1 \over 6}}}\)
\(\small{\frac{{{6^{{\textstyle{1 \over 2}}}}}}{{{6^{\text - 1{\textstyle{1 \over 2}}}}}} = {6^{{\textstyle{1 \over 2}} + 1{\textstyle{1 \over 2}}}} = {6^2} = 36}\)
\(\small{{\left( {\frac{{{6^{{\textstyle{1 \over 3}}}}}}{{{6^{{\textstyle{1 \over 2}}}}}}} \right)^6} = {\left( {{6^{{\textstyle{1 \over 3}} - {\textstyle{1 \over 2}}}}} \right)^6} = {6^{2 - 3}} = {6^{ \text- 1}} = {\textstyle{1 \over 6}}}\)
\(\small{{\left( {\frac{6}{{{6^{{\textstyle{1 \over 6}}}}}}} \right)^{1{\textstyle{1 \over 5}}}} \cdot {6^{\text - 1}} = {\left( {{6^{1 - {\textstyle{1 \over 6}}}}} \right)^{{\textstyle{6 \over 5}}}} \cdot {6^{\text - 1}} = {6^1} \cdot {6^{ \text- 1}} = {6^0} = 1}\)