If power P, length L and time T are chosen as base quantities, give dimensional formula of mass.

Power P =

Work / Time = Force * distance/ TIme

= mass *  accelaration * distance/Time

= mass * (distance/time²) * distance/time

= mass * distance³ * time^-3

Therefore, [P] = [ML³T^-3]

Let mass M be P^xL^yT^z .

Hence, M = [ML³T^-3]^xL^yT^z  = M^xL^(3x+y)T^(-3x+z)

Write the LHS as M¹L⁰T⁰. Then, by comparing the exponents on both sides, we get 3 equations :

x = 1..............(1)

3x+y = 0................(2)

-3x+z = 0...................(3)

Using (1) in (2), y = -3

Using (1) in (3), z=3.

Therefore, M = P¹L^-3T³

Hi

units of P = W = kg.m^2/s^3
             L = m
             T = s

For getting the dimensional formula for mass (kg) assume :
   P^p L^l T^t = kg

putting the units in place of P, L and T
   (kg.m^2/s^3)^p m^l s^t = kg
 
Comparing the units on LHS and RHS :
 (for kg) p=1
(for s) -3p+t = 0
               t = 3p = 3
(for m) 2p + l=0
              l = -2p = -2

Then we get the formula as : [P] [L]^-2 [T]^3 = kg