To simplify the given expression:

[ \frac{x^2 \cdot \sqrt[3]{x \cdot x^2 + x^4}}{\sqrt[4]{x^5}} ]

Let's proceed step-by-step.

Step 1: Simplify the Cube Root in the Numerator

Inside the cube root, we have $x \cdot x^2 + x^4$. This can be simplified as:

$x \cdot x^2 = x^3$

So, inside the cube root, we get:

[ \sqrt[3]{x^3 + x^4} = \sqrt[3]{x^3(1 + x)} = x \cdot \sqrt[3]{x^2 + x^3}