1. The problem is to understand how to express $x$ as $e$ raised to the power of $-2$. 2. The expression $x = e^{-2}$ means that $x$ is equal to the exponential function with base $e$ (Euler's number, approximately 2.718) raised to the power of $-2$. 3. This can be rewritten using the property of exponents: $$e^{-2} = \frac{1}{e^2}$$ which means $x$ is the reciprocal of $e$ squared. 4. So, $x = e^{-2}$ is a compact way to write $x = \frac{1}{e^2}$. 5. This is commonly used in mathematics to represent decay or decrease exponentially. Final answer: $$x = e^{-2} = \frac{1}{e^2}$$