Final answer:
The dimensional formula of mass is [M] = [L]^-1[M]^(3/2)[T]^-1/2.
Step-by-step explanation:
The dimensional formula of mass can be derived by equating the dimensions of the given quantities. The speed of light (c) has dimensions of [L][T]^-1, the gravitational constant (G) has dimensions of [M]^-1[L]^3[T]^-2, and Planck's constant (h) has dimensions of [M][L]^2[T]^-1. By equating these dimensions to the dimensions of mass (M), we can solve for the powers of L, M, and T.
Therefore, the dimensional formula of mass is [M] = [L]^-1[M]^(3/2)[T]^-1/2.
In the derived formula, [L]^-1 represents a negative exponent for length, [M]^(3/2) represents a square root of mass, and [T]^-1/2 represents a square root of time.