What are the dimensions of Work and Power?

Work ($W$) is defined as force ($F$) multiplied by distance ($d$).

$$W = F \cdot d$$

Force is defined as mass ($m$) multiplied by acceleration ($a$).

$$F = m \cdot a$$

The fundamental dimensions are Mass ($M$), Length ($L$), and Time ($T$).
The dimensions of mass are $[M]$.
The dimensions of distance are $[L]$.
The dimensions of acceleration are $[L][T]^{-2}$ (since acceleration is change in velocity over time, and velocity is change in distance over time).

Substitute the dimensions for force:

$$[F] = [M] \cdot [L][T]^{-2} = [M][L][T]^{-2}$$

Now, substitute the dimensions for work:

$$[W] = [F] \cdot [d] = ([M][L][T]^{-2}) \cdot [L] = [M][L]^2[T]^{-2}$$

The dimensions of Work are $\boxed{[M][L]^2[T]^{-2}}$.

Power ($P$) is defined as work ($W$) done per unit time ($t$).

$$P = \frac{W}{t}$$

From Step 1, the dimensions of Work are $[M][L]^2[T]^{-2}$.
The dimensions of time are $[T]$.

Substitute the dimensions for power:

$$[P] = \frac{[M][L]^2[T]^{-2}}{[T]} = [M][L]^2[T]^{-2}[T]^{-1} = [M][L]^2[T]^{-3}$$

The dimensions of Power are $\boxed{[M][L]^2[T]^{-3}}$.