Unit Conversion I'm working with the following equation: Rs [mg/(cm^2 . day)] = K [units not given] * X [mg/cm^2] * shearstress^0.58 [dyne/cm^2] As far as I can tell, 1 dyne = 10^-5 Newtons. The first issue I'm having is determining the units of K. The fact that shearstress is raised to the power of 0.58 is confusing me in this regard, as I'm not sure whether to include this in the dimensional analysis. The second thing I'm looking to do is to convert the units of the entire equation to [μg/(cm^2 . hour)]. How would I go about this conversion? Thanks very much in advance for any advise, and please let me know if I need to provide any more information.

You are correct 1 dyne =10^{-5} Newton. You can't raise something with units to a fractional power, so you must be intended to measure the shear stress in dyne/cm^2 and raise the value to the power $0.58$. The shear stress must really be divided by a standard value of 1 dyne/cm^2, and you should consider that term dimensionless. For dimensional analysis we can then ignore that term.

Now match up the units in the rest of the equation to find the units of K. To convert to $\mu g$, you use the fact that 1 mg=1000 $\mu$g, so terms with mg in the numerator get multiplied by $1000$. You also need to convert days to hours, so where you see day you should put 24 hours.