\(\frac{AB^4}{AC^4}=\frac{\left(AB^2\right)^2}{\left(AC^2\right)^2}=\frac{\left(BH\cdot BC\right)^2}{\left(CH\cdot BC\right)^2}=\frac{BC^2}{CH^2}=\frac{BE\cdot AB}{CF\cdot AC}=\frac{BE}{CF}\cdot\frac{AB}{AC}\Leftrightarrow\frac{AB^3}{AC^3}=\frac{BE}{CF}\)