Chapter 3 - Polynomial and Rational Functions - Summary Exercises on Solving Equations and Inequalities - Exercises - Page 382: 11

$\pm\frac{1}{8}$

Step 1. Start from the given equation $x^{2/3}+\frac{1}{2}=\frac{3}{4}$, we have $x^{2/3}=\frac{3}{4}-\frac{1}{2}\longrightarrow x^{2/3}=\frac{1}{4}$. Step 2. Raise both side to the 3rd power, we have $x^2=(\frac{1}{4})^3$, thus $x=\pm(\frac{1}{4})^{3/2}=\pm\frac{1}{8}$