How can collission theory of chemical reaction and Law of mass action be connected?
For exponentiation, we can say that it is actually repeated multiplication. Comparing two cases:


$$\ce{A + B -&gt; AB}$$
Here, the rate expression is $r=K[\ce{A}][\ce{B}]$. This is because one molecule of $\ce{A}$ and one molecule of $\ce{B}$ is needed for the product to form.
$$\ce{2A + B -&gt; A2B}$$
First, write it in this way: $$\ce{A + A + B -&gt; A2B}$$
Now, rate expression is $r=K\ce{[A][A][B]}$.
That's it - $r=K[\ce{A}]^2[\ce{B}]$


An intuitive starting point for me to understand why concentrations are multiplied is probably to connect it with multiplication theorem in probability (for independent events).