Which expression is equivalent to `\frac{18x^{2}y^{5}}{\left(3xy\right)^{2}}`for all values for `x` and `y` where the expressi
on is defined?
The expression is equal to `18x^{2}y^{5}`.
Explanation:
To simplify the given expression, we start by simplifying the denominator `\left(3xy\right)^{2}`:
`(3xy)^{2}` is the same as `3^{2} \cdot x^{2} \cdot y^{2} = 9x^{2}y^{2}`.
Now, we can rewrite the original expression as:
`\frac{18x^{2}y^{5}}{9x^{2}y^{2}}`
Next, we simplify the fraction by cancelling out common terms in the numerator and denominator:
`= 2y^{3}`
Therefore, the expression `\frac{18x^{2}y^{5}}{\left(3xy\right)^{2}}` simplifies to `2y^{3}`.