$(12$ points$)$ Use the arc length formula $s={\displaystyle \underset{a}{\overset{b}{}}}\sqrt[\phantom{2}]{1+(\frac{dy}{dx}{)}^2}dx$ to find the length of the curve $y=\frac{8}{3}{x}^{\frac{3}{2}}$ from $x=0$ to $x=3.$ Give your answer to two decimal places.