To find the area of a rectangle, we use the formula for area [tex]\( A \)[/tex]:
[tex]\[
A = \text{width} \times \text{length}
\][/tex]
For this particular problem, we are given the width and length as expressions in terms of [tex]\( n \)[/tex]:
- Width: [tex]\( 4n^2 \)[/tex]
- Length: [tex]\( 3n^3 \)[/tex]
Putting these into our formula, we compute the area:
[tex]\[
A = (4n^2) \times (3n^3)
\][/tex]
Next, we multiply the constants and the powers of [tex]\( n \)[/tex] separately:
1. Multiply the constants:
[tex]\[
4 \times 3 = 12
\][/tex]
2. Multiply the powers of [tex]\( n \)[/tex]:
[tex]\[
n^2 \times n^3 = n^{2+3} = n^5
\][/tex]
Combining these results, we get the area:
[tex]\[
A = 12n^5
\][/tex]
Hence, the area of the rectangle is:
[tex]\[
\boxed{12 n^5}
\][/tex]
