The simplified equivalent forms of the given rational functions for $x \neq 2$ are:

1. For $f(x) = \frac{x^3 - 2^3}{x - 2}$, the equivalent function is: $f(x) = x^2 + 2x + 4$

2. For $g(x) = \frac{x^4 - 2^4}{x - 2}$, the equivalent function is: $g(x) = (x + 2)(x^2 + 4)$

Would you like further details or any additional questions?

Here are five related questions to explore:

1. How do you compute the limit of $f(x)$ as $x \to 2$?
2. Why is factoring useful in simplifying limits involving rational functions?
3. What happens if you directly substitute $x = 2$ into $f(x)$ and $g(x)$?
4. How would you use L'Hopital's Rule to evaluate these limits?
5. Can these rational functions have any other points of indeterminacy?

Tip: Always check for common factors in rational functions to simplify them before calculating limits.