[tex]\bf \sqrt{\cfrac{80w^3}{9}}\qquad
\begin{cases}
80=2\cdot 2\cdot 2\cdot 2\cdot 5\\
\qquad 2^2\cdot 2^2\cdot 5\\
\qquad (2^2)^2\cdot 5\\
w^3=w^{2+1}\\
\qquad w^2\cdot w^1\\
9=3\cdot 3\\
\qquad 3^2
\end{cases}\implies \sqrt{\cfrac{(2^2)\cdot 5\cdot w^2\cdot w^1}{3^2}}
\\\\\\
\cfrac{\sqrt{(2^2)\cdot 5\cdot w^2\cdot w^1}}{\sqrt{3^2}}\implies \cfrac{2^2\cdot w\sqrt{5\cdot w^1}}{3}\implies \cfrac{4w\sqrt{5w}}{3}[/tex]
