Time \(\propto c^{x} G^{y} h^{z} \Rightarrow T = k c^{x} G^{y} h^{z}\)

Putting the dimensions in the above relation

\(\left[M^{0}L^{0}T^{-1}\right] = \left[L T^{-1}\right]^{x} \left[M^{-1} L^{3} T^{-2}\right]^{y} \left[M L^{2} T^{-1}\right]^{z}\)

\(\left[M^{0} L^{0} T^{-1}\right] = \left[M^{-y+z} L^{x+3y+2z} T^{-x-2y-z}\right]\)

Comparing the powers of M, L and T

-y + z = 0 …(i)

x + 3y + 2z = 0 …(ii)

-x - 2y - z = 1 …(iii)

On solving equations (i) and (ii) and (iii)

\(x = \frac{-5}{2}, y = z = \frac{1}{2}\)

Hence dimension of time are \(\left[G^{1/2} \hbar^{1/2} c^{-5/2}\right]\)