Chapter 6 Rational Exponents and Radical Functions - 6.6 Solve Radical Equations - Guided Practice for Example 1 - Page 452: 1

$$x=512$$

We solve the equation using the rules of exponents and radicals. Note, if we wanted to check our solution, we could plug the value we get back into the original equation to see if it yields a true statement. Solving the equation, we find: $$\sqrt[3]{x}-9=-1\\ \sqrt[3]{x}=8 \\ x=512$$