Answer:
W = 2*x^3*y^6
Step-by-step explanation:
For this problem, we need to use the relationship:
a^x/a^y = a^(x - y)
For a rectangle with length L and width W, the area is:
A = L*W
We know that in this case we have:
A = 28*x^6*y^9
and:
L = 14*x^3*y^3
We want to find the value of W.
Using the above equation, we have that:
A = 28*x^6*y^9 = L*W = (14*x^3*y^3)*W
28*x^6*y^9 = (14*x^3*y^3)*W
We can solve this for W by isolating it in the right side.
First, let's divide by 14 in both sides to get:
(28*x^6*y^9)/14 = (14*x^3*y^3)*W/14
(28/14)*x^6*y^9 = (14/14)*x^3*y^3*W
2*x^6*y^9 = x^3*y^3*W
Now let's divide by x^3 in both sides to get:
(2*x^6*y^9)/x^3 = (x^3*y^3*W)/x^3
2*(x^6/x^3)*y^9 = (x^3/x^3)*y^3*W
Now we use the relationship that is in the beginning:
2*x^(6 - 3)*y^9 = y^3*W
2*x^3*y^9 = y^3*W
Now let's divide by y^3 in both sides:
(2*x^3*y^9)/y^3 = (y^3*W)/y^3
2*x^3(y^9/y^3) = (y^3/y^3)*W
2*x^3*y^(9 - 3) = W
2*x^3*y^6 = W
The width of the rectangle is given by the equation:
W = 2*x^3*y^6
