SI units and multiplication?

Question

If I have for example kg m^-3 and I have a sum which involves (kg m^-3 x m x m) does this make kg m^-5 or does it cancel to kg m.

Answer 1

The units "kg m^-3" is kg/m^3 therefore if you multiply by m^2 then the units would be kg/m

Answer 2

benabean87's answer, which is 'kg m^-1', is correct.
Quite a few people answer 'kg m', which is the result of a manipulation error. When we have the equation 'kg m^-3 m^2', it can be rewritten as 'kg/m^3 * m^2', which these people probably have done. However, they simplify this to 'kg m', which is wrong. If you recall your maths lessons on indices, dividing indices is simply a matter of subtracting their powers. For example, x^10/x^3 = x^(10-3) = x^8. As such, m^2/m^3 = m^(2-3) = m^-1. Remember that here, m^2 is in the numerator and m^3 in the denominator, not the other way round.
The simpler way which benabean87 has used, is to simply multiply the indices, which is basically adding the powers together. So, m^-3 * m^2 = m^(-3+2) = m^-1.
In short, kg m^-3 * m * m = kg m^-1. If you are confused about the laws of indices you might want to read up more about it on the web.

Answer 3

expanding out it becomes
= kg x m^-3 x m x m
= kg x m^-3 x m^2
to get final indice on the 'm', we add the indices together:

= kg x m^-1

= kgm^-1

Answer 4

If I understand you correctly, it would cancel to give you kg/m.

Answer 5

only quantities having same units are added or subtracted remembered above sum is not possible as units of both are different eg distance is added and subtracted with distance only not velocity OK.