d) \( \left(-\frac{1}{5}\right)^{-3}= \)

To solve \( \left(-\frac{1}{5}\right)^{-3} \), we first rewrite the negative exponent. This means we take the reciprocal, so it becomes \( \left(-\frac{1}{5}\right)^{-3} = \left(-\frac{5}{1}\right)^{3} \). Now, calculating \( \left(-5\right)^{3} \) gives us \(-125\). Thus, \( \left(-\frac{1}{5}\right)^{-3} = -125\). When working with negative bases and exponents, remember that the sign will depend on whether the exponent is odd or even. Here, since the exponent is odd, the result is negative. This little trick can save you from errors! Also, when dealing with negative fractions, keep an eye on how the negative sign is treated in calculations. It’s easy to overlook your signs when inverting fractions or operating with exponents. Always double-check your steps to avoid common mistakes!