Simplify the following expression: \[ \frac{18 k^{5}}{\left(3 k^{2}\right)^{3}} \]

To simplify the expression \(\frac{18 k^{5}}{\left(3 k^{2}\right)^{3}}\), we start by simplifying the denominator. First, calculate \((3 k^{2})^{3}\): \[ (3 k^{2})^{3} = 3^{3} (k^{2})^{3} = 27 k^{6} \] Now, substitute this back into the expression: \[ \frac{18 k^{5}}{27 k^{6}} \] Next, we can simplify the coefficients and the powers of \(k\). Start with the coefficients: \[ \frac{18}{27} = \frac{2}{3} \] Now, simplify the powers of \(k\): \[ \frac{k^{5}}{k^{6}} = k^{5-6} = k^{-1} = \frac{1}{k} \] Putting it all together, we have: \[ \frac{2}{3} \cdot \frac{1}{k} = \frac{2}{3k} \] Thus, the simplified expression is: \[ \frac{2}{3k} \]