A rectangle has width [tex]\(4n^2\)[/tex] and length [tex]\(3n^3\)[/tex]. Determine the area of the rectangle.

A. [tex]\(12n^5\)[/tex]
B. [tex]\(7n^5\)[/tex]
C. [tex]\(7n^6\)[/tex]
D. [tex]\(12n^6\)[/tex]



Answer :

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]