Chapter 1 - Equations and Inequalities - 1.6 Other Types of Equations and Applications - 1.6 Exercises - Page 148: 86

$\{0,\frac{1}{81}\}$

Step 1. Given the equation as $3(x)^{3/4}=(x)^{1/2}$ Step 2. Raise both sides to the 4th power to get: $81(x)^3=x^2$ or $81x^3-x^2=0$ which gives $x=0,\frac{1}{81}$ Step 3. Check answers in the original equation: $\{0,\frac{1}{81}\}$ fit.