Question

the balance equation for the decomposition of Al(ClO3)3

Answer 1

It will decompose into \[Al ^{3+}\] and \[ClO _{3}^{-1}\]

From there, you're gonna want to make sure both sides have the same amount of each element. Rule of thumb is balance in this order: polyatomics, then carbons, then hydrogens, then oxygens

Answer 2

Most likely the decomp would produce aluminum chloride and oxygen gas. Glory has given you a dissociation, as if it dissolved in water, not a true decomposition.