The sentence "x is directly proportional to y and is inversely proportional to the cube of z" can be written as the following equation:

$x = k \cdot \frac{y}{z^3}$

where $k$ is the constant of proportionality.

Do you have any questions or need more details?

Here are 5 related questions for further understanding:

1. What happens to $x$ if $y$ is doubled while $z$ remains the same?
2. How does changing $z$ affect $x$ if $y$ is constant?
3. What is the significance of the constant $k$?
4. Can you explain how to derive the formula for inverse proportionality?
5. What would the equation look like if $x$ were inversely proportional to $z^2$ instead of $z^3$?

Tip: Always keep in mind how direct and inverse proportionality affect variables when they change—direct proportionality means they increase or decrease together, while inverse proportionality means one increases as the other decreases.