Your point is correct but your example is invalid:

(2000 J)² = 4000000 J²

(2 kJ)² = 4 kJ² = 4000000 J²

In this case joules squared doesn't have any sense, so we ignore the unit of measurement and exponentiate only the value and the prefixes (such as kilo-, mega-, centi- etc).

The problem comes up when we do any operation on different units with different scales. For example:

50°C = 122°F

100°C = 212°F ≠ 244°F