$($DTFT$)$ Consider two discrete$-$time LTI systems with impulse responses

$h_1[n]=(-\frac{1}{3}{)}^{n}u[n]$ and $h_2[n]=(\frac{1}{5}{)}^{n}u[n]$

$($a$)(10$ pts$)$ What is the Fourier transform $H_1(e^j)$ of $h_1[n]?$

$($b$)(10$ pts$)$ What is the Fourier transform $H_2(e^j)$ of $h_2[n]?$

$($c$)(10$ pts$)$ If the interconnection of the two systems is shown below. What is the overall frequency response $H(e^j),$ the Fourier transform of the overall impulse response $h[n]?$

$($d$)(15pts)$ What is the overall impulse response $h[n]$ for the system in part $($c$)?$