For an ideal gas undergoing an adiabatic process, the relationship between pressure and volume is given by $PV^\gamma = \text{constant}$. From the ideal gas equation, $PV = nRT$, we can write $V = \frac{nRT}{P}$. Substituting this into the adiabatic equation: $P \left(\frac{nRT}{P}\right)^\gamma = \text{constant}$ $\implies P^{1 - \gamma} T^\gamma = \text{constant}$. Also, the relationship between temperature and volume is $TV^{\gamma - 1} = \text{constant}$. Therefore, the correct factor is $P^{1 - \gamma} T^\gamma$.