The image shows a rectangular plot of land that is marked in red, which is going to be sold. The dimensions of the land are given in the form of mathematical expressions. The problem asks for the area of the land.

To calculate the area of a rectangle, we multiply the length by the width.

The length is given as: $\frac{2^7}{5^5} \, \text{meters}$ The width is given as: $\frac{5^8}{5^7} \, \text{meters}$

Let's first simplify these expressions:

1. Simplify the length: $\frac{2^7}{5^5}$
2. Simplify the width: $\frac{5^8}{5^7}$

After that, we multiply the simplified expressions to find the area.

I'll calculate this now. Simplifying the given expressions from sympy import symbols, simplify

Define the powers

length = (27)/(55) width = (58)/(57)

Calculate the area (length * width)

area = length * width area_simplified = simplify(area)

area_simplifiedThe area of the land is approximately $0.205 \, \text{square meters}$.

Would you like further explanation or have any additional questions on this topic?

Here are 5 related questions:

1. How do you convert square meters to other units like square kilometers?
2. What would happen if the dimensions were in different units (like centimeters)?
3. How do you calculate the perimeter of this rectangular land?
4. What is the significance of simplifying the expressions in this problem?
5. How do you calculate the area of land if the shape were a triangle instead of a rectangle?

Tip: When dealing with exponents in expressions, it’s often useful to simplify them before calculating, as it makes the calculations easier and more accurate.