Let $\sigma=h^\alpha k^\beta c^\gamma$, then equating dimensions of both sides, we have

$\left[ MT ^{-3} K ^{-4}\right]=\left[ ML ^2 T ^{-1}\right]^\alpha\left[ ML ^2 T ^{-2} K ^{-1}\right]^\beta\left[ LT ^{-1}\right]^\gamma$

$\alpha+\beta=1 \quad...(i)$

$2 \alpha+2 \beta+\gamma=0 \quad \ldots (ii)$

$-\alpha-2 \beta-\gamma=-3 \quad \ldots (iii)$

In Eq. $(i)$, we multiplying with $2$, we get

$2 \alpha+2 \beta=2 \ldots(iv)$

Now, subtracting Eq. $(ii)$ from Eq. $(iv)$,

we get

$2 \alpha-2 \alpha+2 \beta-2 \beta+\gamma=0-2$

$\gamma=-2$

Now, putting the value of $\gamma$ in Eq. $(iii)$, we get

$\alpha+2 \beta=5 \ldots( v )$

And solve the Eq. $(i)$ and $(v)$, we get $\alpha=-3, \beta=4$

So, $\alpha=-3, \beta=4$ and $\gamma=-2$