Constant terms with powers and roots

In (Axp+Bxq)n, the outer exponent n must be a positive integer. The powers p,q inside the summands may be negative or fractional; a fractional inner power does not make this a non-integer binomial expansion. The general term contains xp(n-r)+qr, because multiplying powers adds exponents. A term is independent of x exactly when that exponent is zero. Write the general term, solve p(n-r)+qr=0, check r in 0,1,,n, then substitute that index into the numerical factors. State x 0 for reciprocals and use x>0 for the root examples here. For (sqrt(x)+1/x)6, x>0, the exponent is 3-3r/2. Hence r=2 and the constant term is 62=15. A zero exponent means a constant term, not a zero coefficient. If the exponent equation gives a noninteger index, there is no constant term; do not round the index.