Solve the equation with rational exponents.
\[
(x-5)^{2 / 3}=64
\]
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is
(Simplify your answer. Use a comma to separate answers as needed.)
B. The solution set is the empty set.

Answer

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Answer

The solution set is \(\boxed{517}\).

Steps

Step 1 ：Given the equation \((x-5)^{2 / 3}=64\).

Step 2 ：Raise both sides of the equation to the power of \(3 / 2\) to get rid of the rational exponent, resulting in \(x - 5 = 64^{3 / 2}\).

Step 3 ：Solve for \(x\) by adding 5 to both sides of the equation, resulting in \(x = 64^{3 / 2} + 5\).

Step 4 ：Calculate the value of \(64^{3 / 2} + 5\) to get the final answer.

Step 5 ：The solution set is \(\boxed{517}\).