6A
$ \,x(t-k) \to System \to y(t)=(k+1)^{2}x(t-k-1)\, $
Proof:
$ x(t) \to System \to y(t)=e^{x(t)} \to Time Shift(t0) \to z(t)=y(t-t0) $
$ \, =e^{x(t-t0)}\, $
$ x(t) \to Time Shift(t0) \to y(t)=x(t-t0) \to System \to z(t)=e^{y(t)} $
$ \, =e^{x(t-t0)}\, $
Both cascades yielded the same outputs, thus $ \,y(t)=e^{x(t)}\, $ is time invariant.
