  We give examples of quaternion and octonion division algebras over a field
$F$ of characteristic $2$ that split over a purely inseparable extension $E$ of
$F$ of degree $\geq 4$ but that do not split over any subextension of $F$
inside $E$ of lower exponent, or, in the case of octonions, over any simple
subextension of $F$ inside $E$. Thus, we get a negative answer to a question
posed by Bernhard M\"uhlherr and Richard Weiss. We study this question in terms
of the isotropy behaviour of the associated norm forms.
