Question

the area of a rectangle is $54x^{9}y^{8}$ square yards. if the length of the rectangle is $6x^{3}y^{4}$ yards, which expression represents the width of the rectangle in yards?
f $9x^{3}y^{2}$
g $48x^{6}y^{4}$
h $9x^{6}y^{4}$
j $60x^{12}y^{12}$
options: j, g, h (selected), f

Explanation:

Step1: Recall area formula for rectangle

The area of a rectangle is given by $A = l \times w$, where $A$ is area, $l$ is length, $w$ is width. Rearranged to solve for width: $w = \frac{A}{l}$

Step2: Substitute given values

Substitute $A = 54x^9y^8$ and $l = 6x^3y^4$ into the formula:
$w = \frac{54x^9y^8}{6x^3y^4}$

Step3: Divide coefficients and variables

First divide the numerical coefficients: $\frac{54}{6} = 9$
Then apply exponent rules for division ($\frac{x^a}{x^b}=x^{a-b}$):
For $x$: $x^{9-3}=x^6$
For $y$: $y^{8-4}=y^4$
Combine the results: $w = 9x^6y^4$

Answer:

H. $9x^6y^4$