Seriously, the c (centi, or 1/100) should be squared, otherwise it makes no sense. Let’s say something is 10 cm x 10 cm. That is:
![\[10 \frac{1}{100} \mathrm{m} \cdot 10 \frac{1}{100} \mathrm{m} = \frac{1}{100} \mathrm{m}^2\]](https://danielkappelle.com/wp-content/ql-cache/quicklatex.com-db475a167ba9b32ad4621225245b24f3_l3.png "Rendered by QuickLaTeX.com")
Whereas 100 cm2 would be
![\[ 100 \cdot \frac{1}{100} \mathrm{m}^2 = 1 \mathrm{m}^2,\]](https://danielkappelle.com/wp-content/ql-cache/quicklatex.com-71299b40853d4411562f7cb554c09a5e_l3.png "Rendered by QuickLaTeX.com")
which is clearly not the same. Hence we should write
![\[100 (\mathrm{cm})^2\]](https://danielkappelle.com/wp-content/ql-cache/quicklatex.com-cdd61679369a973be0a76090f47e3765_l3.png "Rendered by QuickLaTeX.com")
and all our problems are solved, yay! This of course goes for all other SI prefixes.