What is the answer if you simplify (-3k^0) ^-4

Anything raised to the zeropower is 1. So k^0 = 1 and you can forget about it.

The expression is now (-3) ^-4.

Anything raised to the - 4 power means 1 / (the same thing raised to the 4 power).

So (-3) ^-4 means 1 / [ (-3) · (-3) · (-3) · (-3) ].

If you slog through that, you should end up with 1 / 81.

You really ought to slog through it, for the practice.