To simplify the expression \(\frac{7x^{-2}y}{9x^8y^{-5}}\), you can use the properties of exponents.
First, combine the variables with the same bases:
\[
\frac{7}{9} \cdot \frac{x^{-2}}{x^8} \cdot \frac{y}{y^{-5}}
\]
Next, simplify each part individually:
\[
\frac{7}{9} \cdot \frac{1}{x^{2+8}} \cdot \frac{y^1}{y^{-5}}
\]
Combine the exponents:
\[
\frac{7}{9} \cdot \frac{1}{x^{10}} \cdot y^{1-(-5)}
\]
Simplify further:
\[
\frac{7y^6}{9x^{10}}
\]
So, \(\frac{7x^{-2}y}{9x^8y^{-5}}\) simplifies to \(\frac{7y^6}{9x^{10}}\).