Question

the area of a rectangle is $54x^{7}y^{8}$ square yards. if the length of the rectangle is $6x^{2}y^{4}$ yards, which expression represents the width of the rectangle in yards?
$9x^{12}y^{12}$
$9x^{5}y^{4}$
$48x^{5}y^{4}$

Explanation:

Step1: Recall area formula

The area formula of a rectangle is $A = l\times w$, where $A$ is area, $l$ is length and $w$ is width. We need to solve for $w$, so $w=\frac{A}{l}$.

Step2: Substitute given values

Given $A = 54x^{7}y^{8}$ and $l=6x^{2}y^{4}$. Then $w=\frac{54x^{7}y^{8}}{6x^{2}y^{4}}$.

Step3: Simplify the expression

Using the quotient - rule of exponents $\frac{a^{m}}{a^{n}}=a^{m - n}$, we have $\frac{54}{6}x^{7-2}y^{8 - 4}=9x^{5}y^{4}$.

Answer:

$9x^{5}y^{4}$