Chapter 9 - Roots and Radicals - 9.5 - Solving Radical Equations - Problem Set 9.5 - Page 425: 55

{$252$}

Step 1: $\sqrt[3] {4x-8}=10$ Step 2: Raising each side of the equation to the power of $3$ and simplifying, we obtain: $(\sqrt[3] {4x-8})^{3}=(10)^{3}$ $4x-8=1000$ Step 3: Solving the equation, we obtain: $4x-8=1000$ $4x=1000+8$ $4x=1008$ $x=\frac{1008}{4}$ $x=252$ Therefore, the solution set of the equation is {$252$}.