$A, B$ are constants with unknown units.
$n$ is an unknown integer.
I have the following:
len is quantity for length
$A \cdot (len)^2 + B$ represent electric potential.
$A \cdot (len)^{n-5}$ it's also represent electric potential.
In my exercise, I know that those expressions are represent the same electric potential(electric potential is continuous function).
Can I tell for sure that $n=7$?
Thanks.
Yes. It does not matter what they are, just that they have the same units. As long as the units match between the two expressions, you are given that $[m^2]=[m^{n-5}],$ which tells you that $n-5=2$