\( 2(x-1)^{2 / 3}=32 \) The solution set is

Solve the equation \( 2(x-1)^{2 / 3}=32 \). Solve the equation by following steps: - step0: Solve for \(x\): \(2\left(x-1\right)^{\frac{2}{3}}=32\) - step1: Divide both sides: \(\frac{2\left(x-1\right)^{\frac{2}{3}}}{2}=\frac{32}{2}\) - step2: Divide the numbers: \(\left(x-1\right)^{\frac{2}{3}}=16\) - step3: Simplify the expression: \(x-1=\pm 16^{\frac{3}{2}}\) - step4: Simplify: \(x-1=\pm 64\) - step5: Separate into possible cases: \(\begin{align}&x-1=64\\&x-1=-64\end{align}\) - step6: Calculate: \(\begin{align}&x=65\\&x=-63\end{align}\) - step7: Rewrite: \(x_{1}=-63,x_{2}=65\) The solution set for the equation \(2(x-1)^{2/3}=32\) is \(x=-63\) and \(x=65\).