Explanation

Time $\propto c^{x}G^{y}h^{z} \Rightarrow T = {kc}^{x}G^{y}h^{z}$ Putting the dimensions in the above relation $\Rightarrow \left\lbrack M^{0}L^{0}T^{1} \right\rbrack = \left\lbrack LT^{- 1} \right\rbrack^{x}\left\lbrack M^{- 1}L^{3}T^{- 2} \right\rbrack^{y}\left\lbrack ML^{2}T^{- 1} \right\rbrack^{z}$ $\Rightarrow {\lbrack M}^{0}L^{0}T^{- 1}\rbrack = \lbrack M^{- y + z}L^{x + 3y + 2z}T^{- x - 2y - z\ }\rbrack$ 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 $\lbrack G^{1/2}h^{1/2}c^{- 5/2}$]