If the velocity of light c, the universal gravitational constant G, and the Planck's constant h are chosen as fundamental units, the dimensions of mass in this system are : 

h^1/2 c^1/2 G^-1/2

[M] = [h^a c^b G^c]

[ML²T^-1]^a [LT^-1]^b [M^-1L³T^-2]^c = [M]

⇒ [M^a-cL^2a+b+3cT^-a-b-2c] = [M]

a-c =1 

2a+b+3c =0

-a-b-2c = 0

On solving for a, b and c, 

a = 1/2 ; b = 1/2 ; c = -1/2

[h^1/2 c^1/2 G^-1/2] = [ML²T^-1]^1/2 [LT^-1]^1/2 [M^-1L³T^-2]^-1/2

[h^1/2 c^1/2 G^-1/2] = [M]