How do I find the quotient of x/2y and (2xy)^2/9xy^3
if top = (x/2y)
and
bottom = [ (2xy)^2/9xy^3 ]
multiply top and bottom by 18 x y^3
To find the quotient of x/2y and (2xy)^2/9xy^3, you need to first simplify both expressions separately and then divide them.
Let's start by simplifying the expressions:
1. Simplifying x/2y:
The expression x/2y can be written as x * (1/2y). Here, we can cancel out the common factor of y:
x * (1/2y) = x * (1/(2 * y)) = x/(2y)
2. Simplifying (2xy)^2/9xy^3:
To simplify (2xy)^2/9xy^3, we need to expand the square of (2xy) and then simplify the expression further:
(2xy)^2 = (2xy) * (2xy) = 4x^2y^2
Now, substitute this into the expression we had:
(2xy)^2/9xy^3 = 4x^2y^2 / 9xy^3
To find the quotient, divide the simplified expressions:
x/(2y) ÷ (4x^2y^2 / 9xy^3)
When dividing fractions, you can multiply by the reciprocal of the second fraction:
x/(2y) ÷ (4x^2y^2 / 9xy^3) = x/(2y) * (9xy^3 / 4x^2y^2)
Now, you can simplify further by canceling out common factors:
x/(2y) * (9xy^3 / 4x^2y^2) = (x * 9xy^3) / (2y * 4x^2y^2)
Now, we can further simplify by canceling out the common factors:
(x * 9xy^3) / (2y * 4x^2y^2) = (9xy^3) / (2 * 4x^2y^2)
Finally, simplify the expression:
(9xy^3) / (2 * 4x^2y^2) = (9xy^3) / (8x^2y^2)
Therefore, the quotient of x/2y and (2xy)^2/9xy^3 is (9xy^3) / (8x^2y^2).