Gavin is subdividing land into two plots, where one plot is in the shape of a square and the other plot is in the shape of a rectangle. The square plot of land has a side length of 6x3 feet, and the rectangular plot of land has a length of 3x5 feet and a width of 7x2 feet. Use the properties of exponents to determine the expression that represents the area for each plot of land. Then analyze which plot of land has a larger area if x is 3
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First, let's calculate the area of the square plot of land:
Area of a square = (side length)^2
Area of square plot = (6x^3)^2 = 36x^6 square feet
Next, let's calculate the area of the rectangular plot of land:
Area of a rectangle = length x width
Area of rectangular plot = (3x^5)(7x^2) = 21x^7 square feet
Now, let's determine which plot of land has a larger area when x = 3:
For the square plot:
Area = 36(3)^6 = 36(729) = 26,244 square feet
For the rectangular plot:
Area = 21(3)^7 = 21(21,087) = 442,017 square feet
Therefore, the rectangular plot of land has a larger area when x = 3.