# why this frequency response is added to the power of e?

From where did this ${\angle}H{(\Omega)}$ came into power of $e$ ?

$H(\Omega)$ is a complex number. $Ae^{j(\Omega t + \phi)}$ is another complex number, expressed in polar format by its magnitude $A$ and phase $\Omega t + \phi$. When you multiply complex numbers in this format, you simply multiply their magnitudes and sum their phases. Thus:
$$H(\Omega)Ae^{j(\Omega t + \phi)} = |H(\Omega)| Ae^{j(\Omega t + \phi \angle H(\Omega))}$$