# What is the area of a rectangle if one side has a length of 12x^3 and the other side has a width of 6x^2?

Jan 3, 2017

The area of the rectangle is $72 {x}^{5}$

#### Explanation:

The formula for the area of a rectangle is:

$A = l \times w$

Where,

$A$ is the area, what we are solving for in this problem.

$l$ is the length which has been given as $12 {x}^{3}$

$w$ is the width which has been given as $6 {x}^{2}$

Substituting these values gives:

$A = 12 {x}^{3} \times 6 {x}^{2}$

Simplifying gives:

$A = \left(12 \times 6\right) \times \left({x}^{3} \times {x}^{2}\right)$

We can multiply the constants and use the rule for exponents to multiply the $x$ terms.

${y}^{\textcolor{red}{a}} \times {y}^{\textcolor{b l u e}{b}} = {y}^{\textcolor{red}{a} + \textcolor{b l u e}{b}}$

This gives:

$A = 72 \times \left({x}^{3 + 2}\right)$

$A = 72 \times {x}^{5}$

$A = 72 {x}^{5}$