When multiplying numbers with the same base, we can add the exponets.
For example, say we had
$$\begin{array}{}
5^2\times5^2\\
25\times25\\
625
\end{array}$$
and really, 625 is 54, so we then come up with the rule
$$\begin{array}{}
5^2\times5^2=5^{2+2} = 2^4
\end{array}$$
Another thing to remember is that this adding exponets only works if the number have the same base. (here they do because they both have 5's. Your question works too because it's all the same base of 7)
Let's put this in your question.
$$\begin{array}{}
7^{765} \times 7^{450} \times 7^{-822} \times 7^{-389}\\
7^{(765)+(450)+(-822)+(-389)}\\
7^{(1215)+(-1211)}\\
7^{(1215)-(1211)}\\
7^{(4)}\\
(7)(7)(7)(7)\\
(49)(49)\\
2401
\end{array}$$
And we get 2401!
