^ for power. ** is usually in a programming setting (but it‘s usually a method and not an operator there.)
\cdot for matrix multiplication and the dot product, \times for cross product and nothing (or *, if I want to write it explicitly and have no convolution in the expression) for regular multiplication.
Ohne Zwiebel find ich schon schlimm, aber ohne Soße?! Ab auf den Scheiterhaufen!!!