FactorPowersByTheirOrder​(AngouriMath.​Entity,​AngouriMath.​Entity.​Variable)

The expression with every factor g^a of it -- a factor of the product or the quotient it is -- to a
constant exponent that is not an integer, of a g tending to 0 or an infinity, replaced by
x^(k a), and the product of the limits L^a of what was taken out; or null if
there is no such factor. k is the limit of x g' / g, the power of x that g behaves like,
taken where it is rational, and L is the limit of g / x^k, taken where it is a positive number.
sin(x)^pi ln(x) at 0 from the right is sin(1/x)^pi ln(1/x) here, and nothing read a power of
sin(1/x) alongside a logarithm, while it is (x sin(1/x))^pi, which tends to 1, times
x^(-pi) ln(1/x), which tends to 0.