Question

The area of a rectangle is 54x y9 3 6x y4 yards, 8 square yards. If the length of the rectangle is which expression represents the width of the rectangle in yards?Answers:9x¹²y¹²9x⁶y⁴324x¹²y¹²324x⁶y⁴

Answer 1

Answer:

9x⁶y⁴

Explanation:

The area of a rectangle is equal to:

$\text{Area }=\text{ Length x Width }$

So, dividend both sides by the length, we get that the width can be calculated as:

$\text{Width = }\frac{\text{ Area}}{\text{ Length}}$

Then, replacing the expression for the Area and the length, we get:

$\text{Width = }\frac{54x^9y^8}{6x^3y^4}$

Now, we will use the following property:

$\frac{a^m}{a^n}=a^{m-n}$

It means that when we divide two numbers with the same base, we subtract the exponents. So, the width is equal to:

$\begin{gathered} \text{Width}=\frac{54}{6}\cdot\frac{x^9}{x^3}\cdot\frac{y^8}{y^4} \\ \text{Width}=9\cdot x^{9-3}\cdot y^{8-4} \\ \text{Width}=9x^6y^4 \end{gathered}$

Therefore, the expression that represents the width of the rectangle in yards is: 9x⁶y⁴