To find the area of a rectangle, we multiply its length by its width.
Given:
Length = 3a square b units
Width = 2ab cube units
Area = Length * Width
Area = (3a square b) * (2ab cube)
To multiply these terms, we can combine the coefficients (3 and 2) and multiply the variables (a square b and ab cube):
Area = 3 * 2 * (a square b) * (ab cube)
Area = 6 * a square b * ab cube
To simplify the expression, we can combine the variables with the same base (a) by adding their exponents:
Area = 6 * a^(1+1) * b^(1+3)
Area = 6 * a^2 * b^4
Therefore, the area of the rectangle is 6a^2b^4 units.