Problem with \mathbb and superscript number

The manual of amsfonts specifies that \mathbb should only be used with capital letters.

What happens when other characters are in the argument of \mathbb is almost random.

Type \mathbb{R}^2, which is more sensible also on a semantic point of view.

The problem would present also with \mathcal.

You probably don’t actually want a blackboard-bold numeral here. There is one in Unicode, so in unicode-math, your code would do exactly what you said.