1. The problem is to calculate $\left(-\frac{1}{2}\right)^7$. 2. When raising a fraction to a power, raise both numerator and denominator to that power: $$\left(-\frac{1}{2}\right)^7 = \frac{(-1)^7}{2^7}.$$ 3. Calculate the numerator: $(-1)^7 = -1$ because an odd power of a negative number remains negative. 4. Calculate the denominator: $2^7 = 128$. 5. Combine numerator and denominator: $$\frac{-1}{128}.$$ 6. Therefore, the final answer is $-\frac{1}{128}$.