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 :

Explanation

`[M^(0)LT^(0)]= [G]^(a)[c]^(b)[h]^(c )`
`implies [M^(0)LT^(0)]=[M^(-1)L^(3)T^(-2)]^(a)[LT^(-1)]^(b)[ML^(2)T^(-1)]^(c )`
`implies [M^(0)LT^(0)]=[M^(-a+c)L^(3a+b+2c)T^(-2a-b-c)]`
On comparing dimensions on both sides,
`-a+c=0" ""........."(i)`
`3a+b+2c=1" "".........."(ii)`
`-2a-b-c=0" "".........."(iii)`
On solving the equations (i), (ii) and (iii) we get the following : `a=(1/2),b= (-3/2)" and "c= (1/2)`.