Find the area of the region enclosed by the functions.
\[
y=x^{4} \text { and } y=8 x
\]
The area of the region enclosed by the two functions is (Type an integer or a simplified fraction.)

Step 1 ：First, we need to find the points of intersection of the two functions. We set \(y = x^4\) and \(y = 8x\) equal to each other to find the x-values where the functions intersect.

Step 2 ：Solving the equation \(x^4 = 8x\), we get \(x^4 - 8x = 0\). Factoring out an \(x\), we get \(x(x^3 - 8) = 0\).

Step 3 ：Setting each factor equal to zero gives us the solutions \(x = 0\) and \(x = 2\).

Step 4 ：The area enclosed by the two functions is the integral from 0 to 2 of the absolute difference of the two functions. We can write this as \(\int_{0}^{2} |8x - x^4| dx\).

Step 5 ：Since \(8x > x^4\) for \(0 < x < 2\), we can simplify the integral to \(\int_{0}^{2} (8x - x^4) dx\).

Step 6 ：Integrating, we get \([4x^2 - \frac{1}{5}x^5]_{0}^{2}\).

Step 7 ：Substituting the limits of integration, we get \(4(2)^2 - \frac{1}{5}(2)^5 - (4(0)^2 - \frac{1}{5}(0)^5) = 16 - \frac{32}{5} = \frac{48}{5}\).

Step 8 ：So, the area of the region enclosed by the functions \(y = x^4\) and \(y = 8x\) is \(\boxed{\frac{48}{5}}\).