Algebra-2

Question Analysis
This problem assesses the student's ability to simplify a division of radical expressions with a cube root.

Key Concept Explanation
When dividing two radicals with the same index, the quotient of the radicands becomes the new radicand. For cube roots, the conditions are that the radicands must be real numbers and the denominator's radicand must be non-zero.

Step-by-step Solution
1. Confirm conditions: Index = 3 (odd); radicands 125z⁴ ∈ ℝ, 5z ≠ 0; same index.
2. Separate coefficients and radicals: