Solution:

The electric potential \( V \) at a point \( P \) due to an electric dipole with dipole moment \( \overrightarrow{p} \) is given by:

\[
V = \frac{k \, \overrightarrow{p} \cdot \overrightarrow{r}}{r^3}
\]

Explanation:
1. Dipole Moment: The dipole moment \( \overrightarrow{p} = q \cdot d \), where \( q \) is the charge and \( d \) is the separation between charges.

2. Position Vector \( \overrightarrow{r} \): This is the vector from the center of the dipole to the point \( P \).

3. Dot Product: The potential depends on the angle between \( \overrightarrow{p} \) and \( \overrightarrow{r} \), hence \( \overrightarrow{p} \cdot \overrightarrow{r} = p r \cos \theta \).

4. Result: The formula is:
\[
V = \frac{k (\overrightarrow{p} \cdot \overrightarrow{r})}{r^3}
\]

This matches the correct answer:
\[
V = \frac{k (\overrightarrow{p} \cdot \overrightarrow{r})}{r^3}
\]