This thread reminded me something that always seemed to me a bit strange on scientific books.
For example, instead of the more straightforward V=m/s definition for velocity there would be V=m*s[sup]-1[/sup].
Is there a reason why this notation is prefered over the other?
It makes the units easier to typeset without using parentheses.
I find that it can also make it easier to cancel units if you’re doing a long calculation on paper, although that’s probably a matter of personal taste.
It also removes the ambiguity of units like kg⋅m[sup]2[/sup]s[sup]−3[/sup]A[sup]−1[/sup]. Without exponents it would be kg⋅m[sup]2[/sup]/s[sup]3[/sup]A which is ambiguous as to whether the A is in the multiplied or divided, or kg⋅m[sup]2[/sup]/(s[sup]3[/sup]A) which is ugly.
And yes, in typesetting even the most technical of work, “ugliness” is a factor. 
I can also be more intuitive to read. Suppose that one chicken produces x eggs in one day. So the unit for the production rate (x) is “eggs per chicken per day”.
Once you are used to the exponent notation, you will read eggs.chicken[sup]-1[/sup].day[sup]-1[/sup] exactly like"eggs per chicken per day"
eggs/chicken/day would work but it is ambiguous.
In contrast eggs/(chicken.day) is less intuitive, because you don’t want to think in terms of “chicken.day”.
Adding to the voices against ugliness, writing 50 Hz as 50/s just looks wrong to me, but 50s[sup]-1[/sup] looks much better.
Equations with a term under the dividend take up two lines of space, which was a real pain in the days when manuscripts were written on a typewriter. Doing everyone on one line was a big help.
And some equations have subscripts as well as superscripts.
5m⁵
____
7vₐ⁴
Today the computer does it all automatically. When every symbol had to be inserted and adjusted by hand anything to make it easier was desirable.
And the units in the denominator might be to some power other than -1, too. If I have something like, say, 1/m[sup]2[/sup], I have to do the superscript anyway, but I don’t need the 1/ part.
Actually, it’s not ambiguous because the division by itself is distributive. Whether you ratio eggs by chicken or chicken by day first, you get the same end result. However, if you add another operand in the mix, the order of operations is ambiguous. This is why prefix or postfix notation is technically superior.
As for the the notation on units, it gets rid of the pure evil that is fractions in complex unit conversions and replaces it with exponents that can just be added together. No more accidentally inverting your conversion so you multiply by 386.4 instead of divide, and show that your steel structure is going to deform into a tangled mass of metal because a butterfly alights upon it. This is especially useful when dealing with non-integer exponents in calculations and brings logarithms into the discussion naturally instead of being treated like some kind of freaky mathematical coincidence that you have to deal with only if you are doing signal analysis, advanced probability, and information or number theory.
Stranger