To determine which quantity has different dimensions, we examine the dimensional formula for each:

1. Work and Energy: Work ($W = \mathbf{F} \cdot \mathbf{d}$) and all forms of energy (kinetic, potential, etc.) have the same dimensions . Since Force has dimensions $[MLT^{-2}]$ and distance is $[L]$, Work and Energy have dimensions of $[ML^2T^{-2}]$ .
2. Torque: Torque is defined as the moment of force ($τ = \mathbf{r} \times \mathbf{F}$) . Its magnitude is force times the perpendicular distance, giving it the same dimensions as work or energy: $[ML^2T^{-2}]$ .
3. Power: Power ($P$) is defined as the rate of doing work ($P = W/t$) . Dividing the dimensions of work ($[ML^2T^{-2}]$) by time ($[T]$) gives the dimensions for power as $[ML^2T^{-3}]$ .

Comparing the results, Power ($[ML^2T^{-3}]$) is the only quantity with dimensions different from the others ($[ML^2T^{-2}]$).