Inverse of modular exponential

Question

We have two numbers $a$ and $b$ and three very large prime numbers $p_1, p_2$ and $n$. We compute $r_1=$ $a^{p_1}$ $mod$ $n$ and $r_2=$ $b^{p_2}$ $mod$ $n$. Now we forget about $a$ and $b$. Is there a way to go from $r_1$ to $r_2$ oblivious of $a$ and $b$, by just knowing $p_1, p_2$ and $n$ without trying to reach $a$. If yes, can this is be extended if $n$ is replaced by $n_1$ and $n_2$, one for each equation ?