soft question - Why aren't units with powers, like cm³, surrounded by parentheses?

Since $\renewcommand{\unit}[1]{\,\mathrm{#1}} 1\unit{dm} = 10^{-1}\unit{m}$, it follows that $1\unit{dm^3} = 10^{-1} \times 10^{-1} \times 10^{-1} \unit{m^3} = 10^{-3} \unit{m^3}$.

However, in regular mathematics the following equation holds true:

$$a\,b^{3} = a\,b\,b\,b$$

By the above, the cube unit should expand as follows:

$$\mathrm{dm^3} = \mathrm{dmmm}$$

While in actual usage (as seen in the second equation) the expansion is $\mathrm{dddmmm}$, which would arise from using $\mathrm{(dm)^3}$ instead.

$$\mathrm{(dm)^3} = \mathrm{dddmmm}$$

So shortly: why aren't parentheses (commonly?) used in units?

Answer

The thing is that $\mathrm{dm}$ is a single symbol, not a combination of two symbols.

Yes, it can be understood in terms of a prefix and a base indicator, but it is still a single symbol. An analogy to the concatenation of variable is inappropriate.

Reference to an authoritative statement:

The grouping formed by a prefix symbol attached to a unit symbol constitutes a new inseparable unit symbol (forming a multiple or submultiple of the unit concerned) that can be raised to a positive or negative power and that can be combined with other unit symbols to form compound unit symbols.

Example: $\renewcommand{\unit}[1]{\,\mathrm{#1}} 2.3\unit{cm^3} = 2.3\unit{(cm)^3} = 2.3 \unit{(10^{–2}\,m)^3} = 2.3 \times 10^{–6} \unit{m^3}$