Input signal $x[n]$ and impulse response $h[n]$ are given. Find $z$ transforms of $x[n]$ and $h[n].$ Using formula $Y(z)=x(z)H(z)$ find $Y(z)$ and then find $y[n].$

$x[n]=u[n]$;$,h[n]={0\mathrm{.}4}^{n}u[n]$;