Notation for Kronecker product of a matrix and itself?

Question

What is the notation for the Kronecker product of a matrix and itself?

In other words, is there a short-hand way I can express the following:

1. $X⊗X$
2. $X⊗X⊗X$
3. $X⊗X⊗X⊗X$

Where $X$ is a matrix?

What I am looking for is analogous to the following when using the multiplication operator:

1. $x$ x $x$ = $x^2$
2. $x$ x $x$ x $x$ = $x^3$
3. $x$ x $x$ x $x$ x $x$ = $x^4$

@IanColey suggests: $X^{⊗n}$

is this correct?