(-0,2)^-4

To evaluate \((-0.2)^{-4}\): 1. Recall that a negative exponent indicates a reciprocal: \[ a^{-n} = \frac{1}{a^{n}} \] 2. So, \[ (-0.2)^{-4} = \frac{1}{(-0.2)^{4}} \] 3. Calculate \((-0.2)^4\): Since the exponent is even, the negative sign will disappear: \[ (-0.2)^4 = (0.2)^4 \] 4. Compute \(0.2^4\): \[ 0.2^2 = 0.04 \] \[ 0.2^4 = (0.2^2)^2 = (0.04)^2 = 0.0016 \] 5. Now, take the reciprocal: \[ \frac{1}{0.0016} = \frac{1}{\frac{16}{10000}} = \frac{10000}{16} = 625 \] **Final answer:** \[ (-0.2)^{-4} = \boxed{625} \]