The problem states that the length of the rectangular field is $2x^2$ and the width is $4x$. We are asked to find the area of the rectangular field.

Step-by-Step Solution:

The area $A$ of a rectangle is given by the formula: $A = \text{Length} \times \text{Width}$ Substituting the given values for length and width: $A = (2x^2) \times (4x)$

Now, multiply the terms: $A = 2x^2 \times 4x = 8x^3$

Thus, the area of the rectangular field is $8x^3$.

Correct Answer:

The correct option is $8x^3$.

Would you like further details or have any questions?

Here are 5 related questions to expand on this topic:

1. How would the area formula change if both length and width were linear terms like $ax + b$?
2. What happens to the area if the length and width are doubled?
3. How do you simplify the product of two polynomials like $(x^2)(x^3)$?
4. If the width were instead $5x^2$, how would the area change?
5. Can you find the perimeter of the rectangle given these dimensions?

Tip: When multiplying expressions with exponents, always add the exponents if the base is the same.