SolveWithPolynomialPowersBelowTheBar​(AngouriMath.​Entity,​AngouriMath.​Entity.​Variable,​System.​Boolean)

A product with a whole negative power of a polynomial in x of
two or more terms among its factors, with every such power written below the bar
and asked again as a question of its own: u^2 (a u^2 + b)^(-3) as
u^2/(a u^2 + b)^3. The gathering of powers on the way into the chain writes
u^3/((a u^2 + b)^3 u) -- the exponential substitution's quotient for Rubi's
1/(b/f^x + a f^x)^3 -- in the first spelling, a product with a power in it,
which no rational rule reads, where the second is a quotient every one of them
reads; the symbolic quadratic was declined for it. A power of the variable alone
is left as it is, since that spelling is read, and SolveAsPolynomialTerm(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean) writes 1/x^n back into it; and a lone power, (a u^2 + b)^(-3), is the
closed rules' as written. Where the quotient was the question one level up -- the
constant-over-a-power branch of SolveAsPolynomialTerm(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean) asks the power
-- the cycle guard declines it and the chain goes on. A rational function of
x only: the rewrite is another pass through the chain, and for
anything else it was a search that found nothing the spelling had hidden.