Write the expression as a single logarithm.
$$\frac{1}{5}{\log }_{8}z+6{\log }_{8}x-{\log }_{8}y$$

Step 1 ：Given the expression $\frac{1}{5}{\log }_{8}z+6{\log }_{8}x-{\log }_{8}y$

Step 2 ：We can use the properties of logarithms to simplify this expression. The properties are as follows:

Step 3 ：1. $a{\log }_{b}c={\log }_b(c^a)$

Step 4 ：2. ${\log }_{b}a-{\log }_{b}c={\log }_b\left(\frac{a}{c}\right)$

Step 5 ：3. ${\log }_{b}a+{\log }_{b}c={\log }_b(ac)$

Step 6 ：Applying these properties, the given expression can be simplified as follows:

Step 7 ：$\frac{1}{5}{\log }_{8}z+6{\log }_{8}x-{\log }_{8}y={\log }_8(z^{1/5})+{\log }_8(x^6)-{\log }_{8}y$

Step 8 ：This can be further simplified using the properties 2 and 3 to:

Step 9 ：${\log }_8\left(\frac{z^{1/5}{x}^6}{y}\right)$

Step 10 ：Final Answer: The expression can be written as a single logarithm as follows:

Step 11 ：$\boxed{{\displaystyle {\log }_8\left(\frac{z^{1/5}{x}^6}{y}\right)}}$