Consider an expression $QV=KPT{L}^{\alpha }$. Where $V,P,T,L$ and volume, pressure, Time and length respectively. The quantity $\left[Q\right]$ has dimension  $M{L}^{-1}{T}^{-1}$ and $K$ is dimension less constant. The value of integer '$\alpha$' is

$$\begin{gathered} \left[Q\right]=\left[\begin{array}{ccc}M& L^{-1}& T^{-1}\end{array}\right],\left[K\right]=\begin{array}{ccc}{M}^0& L^0& T^0\end{array} \\ \left[V\right]=\left[\begin{array}{ccc}{M}^0& L^3& T^0\end{array}\right],\left[P\right]=\begin{array}{ccc}M& L^{-1}& T^{-2}\end{array} \\ \left[T\right]=\left[\begin{array}{ccc}{M}^0& L^0& T^1\end{array}\right],\left[l\right]=\begin{array}{ccc}{M}^0& L^1& T^2\end{array} \end{gathered}$$

$$\begin{gathered} Substitute, \left[Q\right]\left[V\right]=\left[K\right]\left[P\right]\left[T\right]{\left[L\right]}^{\alpha } \\ \Rightarrow \left[\begin{array}{ccc}M& L^{-1}& T^{-1}\end{array}\right]\left[\begin{array}{ccc}{M}^0& L^3& T^0\end{array}\right]=\left[\begin{array}{ccc}{M}^0& L^0& T^0\end{array}\right]\left[\begin{array}{ccc}M& L^{-1}& T^{-2}\end{array}\right]\left[\begin{array}{ccc}{M}^0& L^0& T^1\end{array}\right]{\left[\begin{array}{ccc}{M}^0& L^1& T^0\end{array}\right]}^{\alpha } \\ \Rightarrow \begin{array}{ccc}M& L^2& T^{-1}=M^{0+1+0+0}{L}^{0-1+0+\alpha }{T}^{0-2+1+0}\end{array} \end{gathered}$$

$\Rightarrow -1+\alpha =2,\left(or\right)\alpha =3$