The dimensions of length are expressed as $G^x{c}^y{h}^z$. G is the universal gravitational constant, c is the speed of light and h is the Planck’s constant. The value of ${\left(\frac{x-y}{z}\right)}^{\frac{1}{x}}$ is 

$$\begin{gathered} \left[G\right]=\left[M^{-1}{L}^3{T}^{-2}\right] \\ \left[c\right]=\left[L{T}^{-1}\right] \\ \left[h\right]=\left[M{L}^2{T}^{-1}\right] \\ \left[M^o{L}^1{T}^o\right]={\left[M^{-1}{L}^3{T}^{-2}\right]}^x{\left[L{T}^{-1}\right]}^y{\left[M{L}^2{T}^{-1}\right]}^z \\ \begin{array}{l}-x+z=0 3x+y+2z=1\\ -2x-y-z=0\\ x=\frac{1}{2},y=-\frac{3}{2},z=\frac{1}{2}\\ {\left(\frac{x-y}{z}\right)}^{\frac{1}{x}}=16\end{array} \end{gathered}$$