Given:
[tex]7^{-\frac{5}{6}}\cdot7^{-\frac{7}{6}}[/tex]
Required: To simplify the given expression.
This is explained thus:
Using the multiplication law and the negative index law of indices, we have:
[tex]\begin{gathered} 7^{-\frac{5}{6}}\cdot7^{-\frac{7}{6}} \\ =7^{-\frac{5}{6}+(-\frac{7}{6})} \\ =7^{-\frac{5}{6}-\frac{7}{6}} \\ =7^{-2} \\ =\frac{1}{7^2} \\ =\frac{1}{49} \end{gathered}[/tex]
Hence, the answer is:
[tex]\frac{1}{49}[/tex]
