An amount of heat passing through a metallic rod in time t is given by `Q=(KA(T_(1)-T_(2))t)/(I)` where k= thermal conductivity
A= Cross sectional area, `T_(1) and T_(2)` are temeprature of hot and cold ends respectively and L= length. So the dimesional formula for k=.....

Explanation

`Q=(KA(T_(1)-T_(2))t)/(L)` is given
`:.k=(QL)/(A(T_(1)-T_(2))t)....(i)`
Where, heat energy `[Q]=M^(1)L^(2)T^(-2)`
Length `[L]=L^(1)`
area `[A]=L^(2)`
differerence of temperature.
`(T_(1)-T_(2))=[DeltaT]=K^(1)`
time `[t]=T^(1)`
Note that here we have included K (for temperature) along with M, L and T. Substituting these dimensional formula in equation (1), we get
`[k]=(M^(1)L^(2)T^(-2)L^(1))/(L^(2)L^(1)T^(1)=M^(1)L^(1)T^(-3)K^(-1)`