The problem asks us to multiply and simplify the expression $(5x\sqrt{2x})(-9\sqrt{10xy})$. We assume that all variables represent nonnegative numbers.

1. Problem Description

The problem asks us to multiply and simplify the expression $(5x\sqrt{2x})(-9\sqrt{10xy})$. We assume that all variables represent nonnegative numbers.

2. Solution Steps

First, we multiply the terms outside the radicals:

$5x \cdot (-9) = -45x$

Next, we multiply the terms inside the radicals:

$\sqrt{2x} \cdot \sqrt{10xy} = \sqrt{2x \cdot 10xy} = \sqrt{20x^2y}$

Now, we combine the results:

$-45x\sqrt{20x^2y}$

We can simplify the radical by factoring out perfect squares:

$\sqrt{20x^2y} = \sqrt{4 \cdot 5 \cdot x^2 \cdot y} = \sqrt{4x^2} \cdot \sqrt{5y} = 2x\sqrt{5y}$

Substituting this back into the expression:

$-45x(2x\sqrt{5y}) = -90x^2\sqrt{5y}$

3. Final Answer

The final answer is $-90x^2\sqrt{5y}$.