I am working through a problem in which I have to prove that a particular $f(n) = \Theta(g(n))$. I know that for this to be true there need to exist positive constants $c_1$, $c_2$, and $n_0$ such that for all $n \geq n_0$, $c_1g(n)\leq f(n) \leq c_2g(n)$. Simply put, the goal is to pick values for the constants such that the above inequality holds. As a side note, $n$ must be a positive integer, and $c_1$ and $c_2$ can be any positive real number, correct? I haven't been able to find clarity over that.
Now, suppose the $f(n)$ has some undefined constants $a$ and $b$, such as $f(n) = n^a + n^b$. Note that this is a throwaway example. My question is this: do we need to define $c_1$ and $c_2$ in terms of the constants $a$ and $b$, or do we need to pick an actual numerical value for $c_1$ and $c_2$, and by extension, values for $a$ and $b$? The former is much more difficult to do.
I apologize in advance for the poor formatting (I simply placed any math in italics, which I know is not correct). This is my first ever post on CS stack exchange. Also, I would like to state that there was a serious attempt at researching into the above, but I couldn't find examples of how to prove $f(n) = \Theta(g(n))$ when $f(n)$ has other constants. If anyone has resources related to this, I would be very grateful.
I would appreciate any and all help. Looking forward to potential responses.