Final answer:
The area of the rectangle is 15x^8y^3.
Step-by-step explanation:
The area of a rectangle is found by multiplying its length by its width. In this case, the length is 3x^2y and the width is 5x^6y^2. To find the area, we can multiply the terms together:
Area = (3x^2y) * (5x^6y^2)
Using the property of exponents for multiplication, we add the exponents when the bases are the same:
Area = 3 * 5 * (x^2 * x^6) * (y * y^2)
Area = 15 * x^(2+6) * y^(1+2)
Area = 15x^8y^3
So, the area of the rectangle is 15x^8y^3.