assume that
$ y[n] = x[n-10] $
unit impulse response
$ h[n] = \delta[n] $
$ y[n] = h[n] $
then we can can a unit impulse response as
$ h[n]= \delta[n-10] $
for the frequency response,
$ F(z) = \sum_{m=-\infty}^{\infty} h[m]e^{jmw} $
$ F(z) = \sum_{m=-\infty}^\infty \delta[m-10]e^{jmw} $
therefore,
$ F(z) = e^{10jw} $
