Question

the area of a rectangle is $56x^{12}y^9$ square yards. if the length is $7x^3y^3$ yards, which expression represents the width of the rectangle in yards?

$43x^9y^6$ \t\t\t\t\t\t$8x^4y^3$
option 1 \t\t\t\t\t\toption 2

$63x^{15}y^{12}$ \t\t\t\t\t\t$8x^9y^6$
option 3 \t\t\t\t\t\toption 4

Explanation:

Step1: Recall area formula for rectangle

Area of rectangle: $A = l \times w$, so $w = \frac{A}{l}$

Step2: Substitute given values

$w = \frac{56x^{12}y^{9}}{7x^{3}y^{3}}$

Step3: Divide coefficients first

$\frac{56}{7} = 8$

Step4: Apply exponent rules for $x$

$x^{12-3} = x^{9}$

Step5: Apply exponent rules for $y$

$y^{9-3} = y^{6}$

Step6: Combine all results

$w = 8x^{9}y^{6}$

Answer:

Option 4. $8x^{9}y^{6}$