Simplify: \( \frac{20 r^{5} s^{2}}{26 r^{5} s^{6}} \)

To simplify the expression \( \frac{20 r^{5} s^{2}}{26 r^{5} s^{6}} \), we start by simplifying the coefficients and the variables separately. First, we simplify the coefficients: \[ \frac{20}{26} = \frac{10}{13} \] Next, we simplify the \( r^{5} \) variables in the numerator and denominator, which cancel each other out, resulting in \( 1 \). Now, we simplify the \( s \) variables: \[ \frac{s^{2}}{s^{6}} = s^{2-6} = s^{-4} \] Putting it all together, we have: \[ \frac{10}{13} \cdot 1 \cdot s^{-4} = \frac{10}{13 s^{4}} \] Thus, the simplified expression is: \[ \frac{10}{13 s^{4}} \]