Final answer:
The area of a rectangle with the length of 2x^3 units and the width of 6x^2 units is 12x^5 square units.
Step-by-step explanation:
The area of a rectangle is the product of its length and width. Given the length as 2x^3 units and the width as 6x^2 units, we can find the area by multiplying these two expressions:
Area = Length × Width
Area = (2x^3) × (6x^2)
To multiply the two expressions, we multiply the coefficients (2 and 6) and add the exponents of x (3 and 2), following the rule of exponents x^m × x^n = x^(m+n).
Area = 2 × 6 × x^{3+2}
Area = 12x^5
The area of the rectangle is 12x^5 units2.