Chapter R - Review of Basic Concepts - R.6 Rational Exponents - R.6 Exercises - Page 65: 103

$2x(2x+3)^{-5/9}(-16x^4-48x^3 -30x^2+9x+2)$

Factor out the least power of the variable expression $2x(2x+3)^{-5/9}$, we have: $4x(2x+3)^{-5/9}+6x^2(2x+3)^{4/9}-8x^3(2x+3)^{13/9}=2x(2x+3)^{-5/9}[2+3x(2x+3)^{4/9+5/9}-4x^2(2x+3)^{13/9+5/9}]=2x(2x+3)^{-5/9}[2+3x(2x+3)-4x^2(2x+3)^2]=2x(2x+3)^{-5/9}[2+6x^2+9x -4x^2(4x^2+12x+9)]=2x(2x+3)^{-5/9}(-16x^4-48x^3 -30x^2+9x+2)$