Which expression is equivalent to 18x^2y^5/(3xy)^2 for all values for x and y where the expression is defined?

Question

A. 3xy^3
B. 3x^3y^3
C. 2y^3
D. 2xy

Answer 1

To simplify the expression, we can divide each term inside the fraction by the term outside the fraction raised to the second power. This gives us \[\frac{18x^2y^5}{(3xy)^2} = \frac{18x^2y^5}{9x^2y^2}.\] Simplifying further, we can cancel a factor of $9x^2$ from the numerator and denominator, as well as a factor of $y^2$: \[\frac{18x^2y^5}{9x^2y^2} = \frac{2y^3}{1}.\] Therefore, the expression is equivalent to $\boxed{2y^3}$.