Let's start by simplifying the expression [tex]-27\sqrt{2} \sin(765^{\circ})[/tex].

Since the sin function has a period of 360°, we can rewrite 765° as 765° - 720° = 45°.

Now, we have [tex]-27\sqrt{2} \sin(45^{\circ})[/tex].

Using the fact that sin(45°) = [tex]\frac{\sqrt{2}}{2}[/tex], we can substitute this value into the expression.

Therefore, [tex]-27\sqrt{2} \cdot \frac{\sqrt{2}}{2}[/tex] which simplifies to [tex]-27 \cdot 2 \cdot \frac{\sqrt{2}}{2}[/tex].

Finally, [tex]-54\sqrt{2}[/tex].

So the final simplified expression is [tex]-54\sqrt{2}[/tex].