gavin is subdividing land into two plots, where one is in the shape of a square and the other is in the shape of a rectangle. The square plot of land has a side length of 6x^3 feet The rectangular plot of land has a length of 3x^5 feet and a width of 7x^2 feet. 1) Use the properties of exponents to determine the expression that represents the area of each plot of land. 2) Then determine which plot of land has the larger area if x=3. make it look like a 10th grader did this
1) The expression that represents the area of the square plot of land is (6x^3)^2.
To simplify this expression, we use the property of exponents that states when you raise a power to a power, you multiply the exponents. So, the expression becomes 6^2 * (x^3)^2 = 36 * x^6.
Therefore, the expression that represents the area of the square plot of land is 36x^6.
The expression that represents the area of the rectangular plot of land is length * width, which is (3x^5)(7x^2).
To simplify this expression, we again use the property of exponents that states when you multiply powers with the same base, you add the exponents. So, the expression becomes 3*7 * (x^5 * x^2) = 21 * x^(5+2) = 21 * x^7.
Therefore, the expression that represents the area of the rectangular plot of land is 21x^7.
2) To determine which plot of land has the larger area when x=3, we substitute x=3 into the expressions we found.
For the square plot of land: 36(3^6) = 36(729) = 26244.
For the rectangular plot of land: 21(3^7) = 21(2187) = 45927.
Since 45927 is greater than 26244, the rectangular plot of land has the larger area when x=3.