Find the area between the curves. \[ y=x^{\frac{11}{10}}, y=9 x^{\frac{1}{10}} \] The area between the curves is (Type an exact answer.)

Step 1 ：Set the two functions equal to each other to find the points of intersection: \(x^{\frac{11}{10}} = 9x^{\frac{1}{10}}\).

Step 2 ：The points of intersection are \(x = 0.0\) and \(x = 9.0\).

Step 3 ：The area between the two curves is given by the integral of the absolute difference of the two functions over the interval defined by the points of intersection.

Step 4 ：Evaluate the integral: \(\int_{0.0}^{9.0} |9x^{\frac{1}{10}} - x^{\frac{11}{10}}| dx\).

Step 5 ：The area between the curves is approximately 43.6814745059987.

Step 6 ：Final Answer: The area between the curves \(y=x^{\frac{11}{10}}\) and \(y=9 x^{\frac{1}{10}}\) is \(\boxed{43.6814745059987}\).