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I am really sorry for the junior question but I have a friend who does not understand this. I have been trying to explain this countless times but he does not understand and is convinced that $$(ms^{-1})^2$$ is (1) below instead of (2):

  1. $ms^{-2}$.
  2. $m^2s^{-2}$.
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I edited to remove the large image; I hope that's fine with you. – Arturo Magidin Sep 13 '11 at 19:02
Since $x^2$ means $xx=x\times x$, then $$(ms^{-1})^2 = (ms^{-1})(ms^{-1}) = ms^{-1}ms^{-1} = mms^{-1}s^{-1} = m^2s^{-2}.$$ – Arturo Magidin Sep 13 '11 at 19:03
Does your friend understand the difference between $(ab)^2$ and $ab^2$? – Srivatsan Sep 13 '11 at 19:05
Thanks for all the help. He understand now. – JFW Sep 14 '11 at 16:31
up vote 5 down vote accepted

$$(a\cdot b)^2 = (a\cdot b)\cdot(a\cdot b)=a\cdot b\cdot a\cdot b=a\cdot a\cdot b\cdot b=a^2\cdot b^2$$

Now set $a=m$ and $b=s^{-1}$.

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Perhaps it will help if you use an example: $m = 4$, $s=2$.

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