How do exponents of a unit of physical quantity affect converting between different prefixes of the same unit?

Question

Let's say, I have some quantities in unit $ \rm kg^{-1/2}$, I now want to express the quantity in $\rm g^{-1/2}$. Do I simply multiply the quantity by $\rm k^{-1/2}$ which is approximately $0.0316$ ?

The way I am going about this is that since $\rm kg^{-1/2}$ can be separated into $\rm k^{-1/2}×g^{-1/2}$, and so the quantity has to 'absorb' $\rm k^{-1/2}$.

I'm asking this question because I tend to run into a lot of units with strange exponents when doing data analysis and need a sanity check.

Answer 1

You probably learned the prefixes

• Mega = $10^6$
• Kilo = $10^3$
• Milli = $10^{-3}$

So, all you have to do is using them in the relationship you are interested in. E.g. $$\pi \frac{(kg)^{1/3} \; \cdot MJ}{(mV)^4} = \pi \frac{(10^3g)^{1/3} \; \cdot (10^6J)}{(10^{-3}V)^4} = \pi \frac{10g^{1/3} \; \cdot 10^6J}{10^{-3/4}V^4} = \ldots $$