$\mathrm{ML}^{-1} \mathrm{~T}^{-2}=\left(\mathrm{LT}^{-1}\right)^\alpha\left(\mathrm{ML}^2 \mathrm{~T}^{-1}\right)^\beta\left(\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right)^\gamma$

$1=\beta-\gamma$      $. . . . . (1)$

$-1=\alpha+2 \beta+3 \gamma$     $. . . . .(2)$ 

$\frac{-2=-\alpha-\beta-2 \gamma}{-3=\beta+\gamma}$   $. . . .(3)$

$\frac{1=\beta-\gamma}{-2=2 \beta} \Rightarrow \beta=-1, \gamma=-2$

$-1=\alpha-2-6 \quad \therefore \alpha=7 $