Chapter 1 - Section 1.4 - Radical Equations; Equations Quadratic in Form; Factorable Equations - 1.4 Assess Your Understanding - Page 118: 71

$x=-\frac{1}{8}$ or $x=-27$

We solve by factoring: $2x^{2/3}-5x^{1/3}-3=0$ $(2x^{1/3}+1)(x^{1/3}-3)=0$ $(2x^{1/3}+1)=0$ or $(x^{1/3}-3)=0$ $2x^{1/3}=-1$ or $x^{1/3}=3$ $x^{1/3}=-\frac{1}{2}$ or $x^{1/3}=3$ $x=(-\frac{1}{2})^3$ or $x=(3)^3$ $x=-\frac{1}{8}$ or $x=27$