Question

the rectangle below has an area of 27y^6 square meters and a length of 9y^4 meters. what is the width of the rectangle? width = meters

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 $A = 27y^{6}$ and $l = 9y^{4}$, then $w=\frac{27y^{6}}{9y^{4}}$.

Step3: Simplify the expression

Using the quotient - rule of exponents $\frac{a^{m}}{a^{n}}=a^{m - n}$ and $\frac{27}{9}=3$, we have $w = 3y^{6-4}=3y^{2}$.

Answer:

$3y^{2}$