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Please could someone explain the reason for using negative superscripts in SI units, and more precisely when to use negative versus positive?

I do not understand, for example, why the volume of a fuel would be given in m3 but heat of combustion would be given in J m-3.

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Negative exponents means per. In countries that were heavily influenced by the British, units such as meters per second would most likely be written $m/s$. In Europe and elsewhere it could be written with negative exponents as $m.s^{-1}$.

In your example $J m^{-3}$ means joules per cubic meter.

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