Languages and Grammar

If $L$ is a language, then the product $L \cdot L$ is denoted by $L^2$. The language product $L^n$ for every $n \in \{0,1,2,…\} is defined as follows:

$$ \begin{aligned} L^0 &= \{\Lambda\}\newline L^n &= L \cdot L^{n-1}, \text{if} \ n > 0 \end{aligned} $$