1. The problem is to simplify the expression $e \times -e^x$. 2. Recall that $e$ is the base of the natural logarithm, approximately equal to 2.718. 3. The expression can be rewritten as $e \cdot (-e^x)$. 4. Using the associative property of multiplication, this becomes $-(e \cdot e^x)$. 5. Since $e \cdot e^x = e^{1+x}$ by the laws of exponents, the expression simplifies to $-e^{x+1}$. 6. Therefore, the simplified form of $e \times -e^x$ is $-e^{x+1}$.