I have this homework question that I'm having difficulties with. Any help would be most welcome.

The pressure, p, and volume, v, of a gas undergoing a polytropic process are related by the equation, $\displaystyle p_1 v_1^n=p_2 v_2^n$ where n is the polytropic index.

If $\displaystyle \frac{p_1 v_1}{T_1}= \frac{p_2 v_2}{T_2}$ determine the expression for $\displaystyle p_1$, in terms of $\displaystyle p_2$, $\displaystyle T_1$, $\displaystyle T_2$, and n.