Find the area of the region bounded by the graphs of the given equations. \[ y=81 x, y=x^{5}, x=0, x=3 \] The area is $\square$.

Step 1 ：We are given the equations \(y=81x\), \(y=x^{5}\), \(x=0\), and \(x=3\). We are asked to find the area of the region bounded by these graphs.

Step 2 ：The area between two curves can be found by integrating the absolute difference of the two functions over the given interval. In this case, the two functions are \(y=81x\) and \(y=x^{5}\) and the interval is \(x=0\) to \(x=3\).

Step 3 ：We need to find out which function is above the other in the given interval to correctly set up the integral. We can substitute a value from the interval into both functions and compare the results. Let's choose \(x=1\) for simplicity. For \(y=81x\), we get \(y=81\) and for \(y=x^{5}\), we get \(y=1\). So, \(y=81x\) is above \(y=x^{5}\) in the interval \(x=0\) to \(x=3\).

Step 4 ：Therefore, the area between the curves is given by the integral from 0 to 3 of \((81x - x^{5})\) dx.

Step 5 ：The result of the integral calculation is 243. This is the area of the region bounded by the graphs of the given equations.

Step 6 ：Final Answer: The area is \(\boxed{243}\).