How to solve this?

$\frac{-2(5x^3y^2)^2}{10xy}$

Fisrt, distribute the square.

$\frac{-2(25x^6y^4)}{10xy}$

Distirbute the -2.

$\frac{-50x^6y^4}{10xy}$

Consider that a variable without a power is the same as that variable to the power of 1: x = x¹

If a variable  with a power is divide by the same variable with a lower power, the powers subtract: x⁶/x³=x^6-3=x³

Simplify.

-50/10=-5

$\frac{-5x^6y^4}{x^1y^1}$

Subtract powers.

$-5x^5y^3$