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.