If the energy, E=G^p h^q c^r , where G is the universal...

$E=G^p h^q c^r$$\begin{aligned}& {\left[\mathrm{M}^1 \mathrm{~L}^2 \mathrm{~T}^{-2}\right]=\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right]^p\left[\mathrm{ML}^2 \mathrm{~T}^{-1}\right]^q\left[\mathrm{LT}^{-1}\right]^r} \\ & =\mathrm{M}^{-p+q} \mathrm{~L}^{3 p+2 q+r} \mathrm{~T}^{-2 p-q-r} \end{aligned}$$$Applying principle of homogeneity of dimensions, we get$$\begin{aligned}& -p+q=1 \\ & 3 p+2 q+r=2 \\ & -2 p-q-r=-2 \end{aligned}$$Add (iii)$ and (iv),p+q=0$Add (ii) and (v), we get$q=\frac{1}{2}$From (ii), we get$p=q-1=\frac{1}{2}-1=-\frac{1}{2}$. Put in (iii), we get$-\frac{3}{2}+1+r=2, \quad r=5 / 2