We have to solve this expression with positive exponents:
[tex]\begin{gathered} 7^{\frac{1}{2}}\cdot7^{-\frac{2}{3}} \\ 7^{\frac{1}{2}-\frac{2}{3}} \\ 7^{\frac{1\cdot3-2\cdot2}{2\cdot3}} \\ 7^{\frac{3-4}{6}} \\ 7^{-\frac{1}{6}} \\ \frac{1}{7^{\frac{1}{6}}} \end{gathered}[/tex]
Answer: 1/7^(1/6)
[tex]\frac{1}{7^{\frac{1}{6}}}[/tex]
