Show that, in general for an isentropic process $($for example, going from station $2$ to station $3$ across an ideal compressor$),$ one may write, for stagnation pressures and temperatures, $$

${}_c=\frac{p_{t3}}{p_{t2}}=(\frac{T_{t3}}{T_{t2}}{)}^{\frac{}{-1}}$