1. **State the problem:** Simplify the expression $-e^{-\ln 21}$. 2. **Recall the properties of logarithms and exponents:** For any positive number $a$ and any real number $x$, $e^{\ln a} = a$. Also, $e^{-x} = \frac{1}{e^x}$. 3. **Apply the exponent rule:** Rewrite $e^{-\ln 21}$ as $\frac{1}{e^{\ln 21}}$. 4. **Simplify using the logarithm-exponent identity:** Since $e^{\ln 21} = 21$, we have $\frac{1}{21}$. 5. **Include the negative sign:** The original expression is $-e^{-\ln 21} = -\frac{1}{21}$. **Final answer:** $$-\frac{1}{21}$$