If the dimensions of length are expressed as G^x c^y h^z; where G, c and h are the universal gravitational constant, speed of light and Planck’s constant respectively, then

$$\begin{gathered} \text{ Length }\propto {\mathrm{G}}^{\mathrm{x}}{\mathrm{c}}^{\mathrm{y}}{\mathrm{h}}^{\mathrm{z}} \\ \mathrm{L}={\left[{\mathrm{M}}^{-1}{\mathrm{L}}^3{\mathrm{T}}^{-2}\right]}^{\mathrm{x}}{\left[{\mathrm{LT}}^{-1}\right]}^{\mathrm{y}}{\left[{\mathrm{ML}}^2{\mathrm{T}}^{-1}\right]}^{\mathrm{z}} \end{gathered}$$
By comparing the power of M, L and T in both sides we get
$-\mathrm{x}+\mathrm{z}=0,3\mathrm{x}+\mathrm{y}+2\mathrm{z}=1\text{ and }-2\mathrm{x}-\mathrm{y}-\mathrm{z}=0$
By solving above three equations we get
$\mathrm{x}=\frac{1}{2},\mathrm{y}=-\frac{3}{2},\mathrm{z}=\frac{1}{2}$