b) \( (-0,2)^{-1}+(0,333 \ldots)^{-2}+(-0,5)^{-3}-(-0,25)^{-4}= \)

To solve the expression \( (-0.2)^{-1} + (0.333\ldots)^{-2} + (-0.5)^{-3} - (-0.25)^{-4} \), we need to evaluate each term step by step. 1. **Calculate \( (-0.2)^{-1} \)**: \[ (-0.2)^{-1} = \frac{1}{-0.2} = -5. \] 2. **Calculate \( (0.333\ldots)^{-2} \)**: The decimal \( 0.333\ldots \) is equivalent to \( \frac{1}{3} \): \[ (0.333\ldots)^{-2} = \left(\frac{1}{3}\right)^{-2} = 3^2 = 9. \] 3. **Calculate \( (-0.5)^{-3} \)**: \[ (-0.5)^{-3} = \frac{1}{(-0.5)^3} = \frac{1}{-0.125} = -8. \] 4. **Calculate \( (-0.25)^{-4} \)**: \[ (-0.25)^{-4} = \frac{1}{(-0.25)^4} = \frac{1}{0.00390625} = 256. \] Now, we can combine all the values: \[ -5 + 9 - 8 - 256. \] Calculating this step-by-step: \[ -5 + 9 = 4, \] \[ 4 - 8 = -4, \] \[ -4 - 256 = -260. \] Thus, the final result of the expression is: \[ \boxed{-260}. \]