Simplify: $\frac{81 x^{9}}{3 x^{15}}$

Step 1 ：Given the expression is \(\frac{81 x^{9}}{3 x^{15}}\).

Step 2 ：Divide the coefficients 81 and 3 to get 27.

Step 3 ：Subtract the exponents 15 from 9 to get -6.

Step 4 ：So, the simplified form of the given expression is \(27x^{-6}\).

Step 5 ：Final Answer: \(\boxed{27x^{-6}}\)