Final answer:
To solve the inequality $e^{x^2+6x+8} > 0$, first factor the quadratic expression inside the exponent. The inequality is true for all real values of $x$.
Step-by-step explanation:
To solve the inequality $e^{x^2+6x+8} > 0$, we can first factor the quadratic expression inside the exponent. The expression $x^2+6x+8$ factors as $(x+2)(x+4)$. Therefore, the inequality can be rewritten as $e^{(x+2)(x+4)} > 0$.
Since the exponential function $e^x$ is always positive for any real value of $x$, the inequality $e^{(x+2)(x+4)} > 0$ is true for all real values of $x$.