I'm assuming that -8 is the only coefficient in the group and the rest of the numbers presented are all exponents.
(-8q³r⁴s²)²
I'd break down the equation for easy understanding.
-8² x (q³)² x (r⁴)² x (s²)²
When an exponent is raised to a power. We multiply the exponents.
64 x q⁶ x r⁸ x s⁴
So the simplified expression of (-8q³r⁴s²)² is 64q⁶r⁸s⁴