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The following equation is in my text book:

$1.01 x10^5kg/m-s^2 \over (0.760m)(9.81m/s^2)$

and the following answer is this:

${1.35x10^4kg/m^3 }$

my question is this: where did the ${m^3}$ come from?

If I multiply .760m and 9.81m then I get ${7.4556m^2}$

even if the numerator has is $m^-1$, wouldn't the law of of exponents state that it's going to be -1 - 2 because you subtract the numerator exponent from the denominator exponent.

Ross Millikan
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Danny Rodriguez
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1 Answers1

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You have the answer in your question. The whole units of the numerator are $\frac {kg}{m\cdot s^2}$. The dash is an unfortunate symbol for multiplication. The numerator has length units of $m^{-1}$, the denominator has length units of $m^2$, so the fraction has length units of $-1-2=-3$. The answer has $m^3$ in the denominator, so length units of $m^{-3}$

Ross Millikan
  • 374,822
  • Thank you so much. You explained it exactly as i needed it. Is there a calculator than can spit out an answer for equations like this? – Danny Rodriguez Nov 02 '16 at 05:13
  • I don't know. You just count powers in the numerator and denominator of each unit. Maybe Alpha knows newtons are $kg \cdot m^2/s^2$ but I don't know. – Ross Millikan Nov 02 '16 at 13:49