It seems you're asking about simplifying or analyzing the expression:

$3 \cdot \sqrt[3]{4x^3} / (5x^5)$

Let me break this down:

1. Simplify the cube root:

   • $\sqrt[3]{4x^3} = x \cdot \sqrt[3]{4}$, because $x^3$ simplifies to $x$ under the cube root.

2. Substitute back into the expression: $\frac{3 \cdot x \cdot \sqrt[3]{4}}{5x^5}$

3. Simplify the terms: Divide $x$ in the numerator by $x^5$ in the denominator: $\frac{3 \cdot \sqrt[3]{4}}{5x^4}$

Final Answer:

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

Would you like me to delve deeper into specific steps?

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5 Related Questions:

1. How do cube roots of variables work in general?
2. What happens if the denominator has multiple terms?
3. Can this expression be written in exponential form?
4. How do fractional exponents compare to roots?
5. Can this expression have a graphical representation?

Tip: Always factor variables fully when working with roots to simplify expressions properly.