Chapter 9 - Roots and Radicals - 9.5 - Solving Radical Equations - Problem Set 9.5 - Page 425: 54

{$8$}

Step 1: $\sqrt[3] {4x-5}=3$ Step 2: Raising each side of the equation to the power of $3$ and simplifying, we obtain: $(\sqrt[3] {4x-5})^{3}=(3)^{3}$ $4x-5=27$ Step 3: Solving the equation, we obtain: $4x-5=27$ $4x=27+5$ $4x=32$ $x=\frac{32}{4}$ $x=8$ Therefore, the solution set of the equation is {$8$}.