# What does it mean for undefined control sequence?

When I use

$(LM)^\ast = (LM)^(0) \ucup (LM)^(1)\ucup (LM)^(2)$


I receive an error:

--this is a undefined control sequence

I need to use (LM)^*= (LM)^0 \ucap (LM)^1 \ucap..

and so on. How should I make it in LaTeX?

There is no symbol \ucup or \ucap; use \cup or \cap. Also, for superscripts (or subscripts that contain more than one token, brace them:
\documentclass{article}
$(LM)^\ast = (LM)^{0} \cup (LM)^{1} \cup (LM)^{2}$