Answer:
We know that the area of the square of side length L is:
A = L*L = L^2
In this case, we know that the area is:
A = 128*x^3*y^4 cm^2
Then we have:
L^2 = 128*x^3*y^4 cm^2
If we apply the square root to both sides we get:
√(L^2) = √( 128*x^3*y^4 cm^2)
L = √(128)*(√x^3)*(√y^4) cm
Here we can replace:
(√x^3) = x^(3/2)
(√y^4) = y^(4/2) = y^2
Replacing these two, we get:
L = √(128)*x^(3/2)*y^2 cm
This is the simplest form of L.
