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My short question: How many $\mathrm{m}^2$ are $\mathrm{nm}^2$? Do I have to interpret it as $\mathrm{nm}^2=(\mathrm{nm})^2=(10^{-9}\mathrm{m})^2=10^{-18}\mathrm{m}^2$ or shall it be $\mathrm{nm}^2=\mathrm{n}(\mathrm{m}^2) = 10^{-9} \mathrm{m}^2$? What is the right convention?

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$\rm nm^2=(nm)^2\neq n(m^2)$, therefore, $\rm nm^2=10^{-18}m^2$. Here, $\rm nm$ represents nanometer and $\rm m$ meter.

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That depends.

If $n$ and $m$ are variables (e.g., standing for an integer each), then the convention is that exponents bind tighter than multiplication-by-juxtaposition, so $nm^2=n(m^2)\ne (nm)^2$.

However, it seems that you mean the unit nanometer (which should be written $\rm nm$ with upright type rather than italic). And for SI units, the convention is that metric prefixes (and their abbreviations) bind tighter than exponentiation, so $\rm nm^2 = (nm)^2 = 10^{-18}\;m^2$.

Thus $nm^2=n(m^2)$, but $\rm nm^2=(nm)^2$.

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thx for your answer. Because I meant SI units I have corrected my question –  tampis Jul 6 '12 at 16:23

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