kA^2s

On the SI specification's mathematical correctness.

This depends on how one views a prefix&unit combination. They may look like a product, particularly when each of the pair has a single-letter symbol (like mA, but not kPa for instance). If they are a product, the claimed meaning of mm² etc would indeed not fit with widely used rules of precedence of products and exponents. 

But what the specification says (as quoted earlier) is that the prefix and unit together form a "new inseperable unit symbol": it is not treated as a product of a numeric multiplier and plain (coherent) unit, but as a single symbol.  So there's no product that needs mathematical rules applied when it's raised to some power: there's just the single symbol such as a kV, mm, MPa etc.  

In this way, there's no mathematical incorrectness about how mm, kA etc behave when put to positive or negative powers. 

Is the unit being discussed an A or A²s. If the derived unit is an A²s, ...

A²s is indeed a derived unit. But does the SI permit prefixing of a compound derived unit? That is, one that includes multiplication, division or exponentiation of unit symbols, not  just a single symbol.  I see nothing saying it does. Consider "Prefixes may be used with any of the 29 SI units with special names with the exception of the base unit kilogram": this permits prefixing the single-symbol units, which are the base units and the 22 specially named derived units. As noted before, it doesn't explicitly forbid prefixing compound units, but doing this would clearly create a trouble if prefixes must be without separator and form a new inseparable symbol, etc, while the parts within a compound unit should be separated from each other. The strongest argument I see, anyway, for whether to prefix compound units, is that there's nothing to say it can be done (or have I missed it?). 


As long as we stick to what's actually said, rather than how we've been used to thinking of it (perhaps from much older practices such as combined prefixes, or everyday practices of writing 10k for 10 000) it appears to me to be an unambiguous system.  Thank you for helping me to dig further into this document's not-crystal-clear depths! I hadn't gone in to some of those details before. 


I'll let you know if the IEC gives a verdict - I wrote a quick note last week, just thinking it wouldn't hurt them to correct it for the next time, even if it's never really going to matter.  I'd be amused if they claim they've got their own system.  But I really doubt they'd formally claim that. 

On the SI specification's mathematical correctness.

This depends on how one views a prefix&unit combination. They may look like a product, particularly when each of the pair has a single-letter symbol (like mA, but not kPa for instance). If they are a product, the claimed meaning of mm² etc would indeed not fit with widely used rules of precedence of products and exponents. 

But what the specification says (as quoted earlier) is that the prefix and unit together form a "new inseperable unit symbol": it is not treated as a product of a numeric multiplier and plain (coherent) unit, but as a single symbol.  So there's no product that needs mathematical rules applied when it's raised to some power: there's just the single symbol such as a kV, mm, MPa etc.  

In this way, there's no mathematical incorrectness about how mm, kA etc behave when put to positive or negative powers. 

Is the unit being discussed an A or A²s. If the derived unit is an A²s, ...

A²s is indeed a derived unit. But does the SI permit prefixing of a compound derived unit? That is, one that includes multiplication, division or exponentiation of unit symbols, not  just a single symbol.  I see nothing saying it does. Consider "Prefixes may be used with any of the 29 SI units with special names with the exception of the base unit kilogram": this permits prefixing the single-symbol units, which are the base units and the 22 specially named derived units. As noted before, it doesn't explicitly forbid prefixing compound units, but doing this would clearly create a trouble if prefixes must be without separator and form a new inseparable symbol, etc, while the parts within a compound unit should be separated from each other. The strongest argument I see, anyway, for whether to prefix compound units, is that there's nothing to say it can be done (or have I missed it?). 


As long as we stick to what's actually said, rather than how we've been used to thinking of it (perhaps from much older practices such as combined prefixes, or everyday practices of writing 10k for 10 000) it appears to me to be an unambiguous system.  Thank you for helping me to dig further into this document's not-crystal-clear depths! I hadn't gone in to some of those details before. 


I'll let you know if the IEC gives a verdict - I wrote a quick note last week, just thinking it wouldn't hurt them to correct it for the next time, even if it's never really going to matter.  I'd be amused if they claim they've got their own system.  But I really doubt they'd formally claim that.