Sure, let's compute the area of the circle.
The formula for the area of a circle is given as:
Area = π * r^2
Here, our radius is given as 3x^3. Let's substitute this in our equation,
Area = π * (3x^3)^2
We have a monomial multiplication where base is same (3x^3), we simply add their exponents. Here, squaring means multiplying the exponent with 2.
Area = π * (3^2) * (x^6)
= 9 * π * x^6
But here we only need to provide a monomial representing the area, for any generic circle with radius 3x^3, without considering the actual numerical value of π. So, our answer shall be,
Area = x^6 units.
Therefore, the number of square units in the area of a circle with radius 3x^(3) units is represented by the monomial x^6.