An exponent is saying to take the base number (here, it's -2), and multiply it my itself that number of times.
So, (-2)⁴ = (-2) * (-2) * (-2) * (-2)
= 4 * (-2) * (-2)
= -8 * (-2)
= 16
If the negative sign were outside the parentheses instead, then the solution would be 2⁴ (which is 16), then negative (so, -16). But in the this case the negative is inside the parentheses.
Hope this helps! :)