No, it's not that easy folks.
Barlows and focal reducers are not simple multipliers or dividers. They each work differently depending on the telescope - optical system- being used, and the design of the 'Barlow'. As a result, they add their own set of aberrations. Combine the two, and thing go to hell in a handbasket.
There is
more than just one design of 'Barlow' multiplier or 'reducer'. Glass types and lens designs vary greatly for both. Many are scope design specific, others only work with a very specific instrument.
Depending on the telescope system, barlow will either work well across the whole field of view, or ONLY the inner area. Same for focal reducers. Couple them and the result is even more dodgy. There will be some combinations of Barlows and reducers that will work with a particular telescope system, but that depends on the type Barlow, the type of reducer AND the telescope system - chances are very slim to get a trifecta.
If you have Powermate and a reducer, then try it out. Only then will you see if the combination works with you scope/scopes. There's no free lunch here either...