The dimensions of $\sigma b^4$ where $\text{'}\sigma \text{'}$ is Stefan's constant and $\text{'}b\text{'}$ is Wien's constant are

According to Stefan's law, the energy $\left(E\right)$ emitted per unit area per unit time is, 

 $E=\mathrm{\sigma }{T}^4 \dots \left(1\right)$
where, $\mathrm{\sigma }$ is Stefan's constant and, $T$ is the temperature. The dimensional equation for above, $\frac{\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right]}{\left[{\mathrm{L}}^2\mathrm{T}\right]}=\mathrm{\sigma }\left[{\mathrm{K}}^4\right]$. So, $\mathrm{\sigma }=\left[\frac{{\mathrm{ML}}^2{\mathrm{T}}^{-2}}{{\mathrm{L}}^2\mathrm{T}}\right]\frac{1}{{\mathrm{K}}^4}$ $\Rightarrow \mathrm{\sigma }=\left[{\mathrm{ML}}^0{\mathrm{T}}^{-3}{\mathrm{K}}^{-4}\right]$

Wien's constant is given as, $b=\mathrm{\lambda }T$, where, $\mathrm{\lambda }$ is the wavelength and $T$ is the temperature. Dimension of $b=\mathrm{LK} \dots \left(2\right)$. From equation ($1$) and ($2$), 
Dimension of $\sigma b^4$,$\therefore \sigma b^4=\left[{\mathrm{ML}}^0{\mathrm{T}}^{-3}{\mathrm{K}}^{-4}\right]\left[{\mathrm{L}}^4{\mathrm{K}}^4\right]$$=\left[{\mathrm{ML}}^4{\mathrm{T}}^{-3}\right]$.