The problem asks to write an equation where $w$ varies jointly with the square of $u$ and the cube of $d$, with $k$ as the constant of proportionality.

In this case, "varies jointly" means $w$ is proportional to the product of the square of $u$ and the cube of $d$. The equation can be written as:

$w = k \cdot u^2 \cdot d^3$

Here, $k$ is the constant of proportionality, $u^2$ represents the square of $u$, and $d^3$ represents the cube of $d$.

Let me know if you'd like more details or have any questions!

Related Questions:

1. What does "joint variation" mean in mathematics?
2. How do you find the constant of proportionality in a joint variation problem?
3. How does this equation change if $w$ varies inversely with another variable?
4. Can a variable vary jointly and inversely in the same equation? If so, how?
5. What are other real-world applications of joint variation equations?

Tip: In joint variation problems, always remember to multiply the terms involving each variable and include the constant of proportionality!