## Ordinal Arithmetic

I've been given this question: Find an explicit order isomorphism between 2×2+6 and 1+3×3.

I'm struggling a bit with notation here I think. We're given a similar example and told that 3={[0],[1],[2]} and the others are defined similarly.

Now, to work out what the sets are, how do I think of these without brackets? I know that multiplication distributes over addition on the left, so if I had 2(2+6) I could rewrite it as 2x2 + 2x6. Is it as simple as working that out, then doing (1+3) x 3 on the right then figuring out the isomorphism between the two sets?