Simplify: \( \frac{18 r^{4}}{48 r^{6}} \)

To simplify the expression \( \frac{18 r^{4}}{48 r^{6}} \), you start by simplifying the coefficients and the variables separately. First, simplify the coefficients: \[ \frac{18}{48} = \frac{3}{8} \] Next, simplify the variable part: \[ \frac{r^{4}}{r^{6}} = r^{4-6} = r^{-2} \] Putting it all together, you get: \[ \frac{3}{8} r^{-2} \] To express \(r^{-2}\) in a positive exponent, remember that \(r^{-2} = \frac{1}{r^{2}}\). Thus, the final simplified form is: \[ \frac{3}{8 r^{2}} \]