Equilibrium constant of a reaction whose order of forward and reverse reaction is not same
I'll try and answer your question, but a &quot;full&quot; answer would take a book.
Given the reaction:
$$\ce{aA + bB &lt;=&gt; cC + dD}$$
Then assuming an elementary reaction in the gaseous state the concentration equilibrium constant always has products over reactants and will be:
$$K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$$
The above equation relies on two very specific assumptions:

The reaction is an elementary reaction which often isn't true and the actual coefficients must be determined experimentally since the reaction occurs in steps.
That concentrations can be used instead of activities.

Formally using activities explains part of your question immediately. For instance if A, B and C are gases and D is a liquid or solid, then the activity of D would be unity by definition.
Now breaking down the equilibrium expression into two rate equations we have:

$r_\mathrm{f}$ - Forward reaction rate
$r_\mathrm{r}$ - Reverse reaction rate
$\ce{a^*, b^*, c^*}$ and $\ce{d^*}$ = experimentally determined coefficients which may or may not be equal to the stoichiometric coefficients
$k_\mathrm{f}$ and $k_\mathrm{r}$ are constants for the forward and reverse reactions respectively.

Now using concentrations instead of activities:
\begin{align}
r_\mathrm{f} &amp;= k_\mathrm{f} \ce{[A]^{a^*}[B]^{b^*}}\\
r_\mathrm{r} &amp;= k_\mathrm{r} \ce{[C]^{c^*}[D]^{d^*}}
\end{align}
and at equilibrium by definition:
\begin{align}
r_\mathrm{f} &amp;= r_\mathrm{r}\\
k_\mathrm{f} \ce{[A]^{a^*}[B]^{b^*}} &amp;= k_\mathrm{r} \ce{[C]^{c^*}[D]^{d^*}}
\end{align}
so:
$$K_c = \frac{k_\mathrm{f}}{k_\mathrm{r}}= \frac{\ce{[C]^{c^*}[D]^{d^*}}}{\ce{[A]^{a^*}[B]^{b^*}}}$$
To determine the coefficients the experimentalist can manipulate the experiment to simply the kinetic expression. For example let $\ce{[A] \gg [B]}$ then $\ce{[A]^{a^*}}$ is essentially a constant.
Does this answer your question?