\sqrt[3]{2g-2h+g}

To simplify the expression \(\sqrt[3]{2g-2h+g}\), you can follow these steps:

Step 1: Combine like terms inside the cube root.
The expression becomes \(\sqrt[3]{3g-2h}\).

Step 2: Take the cube root.
To calculate the cube root, you need to find a number that, when raised to the power of 3, gives the value inside the cube root. Let's call this number \(x\).
So, \(x^3 = 3g-2h\).

Step 3: Solve for \(x\).
Raise both sides of the equation to the power of \(\frac{1}{3}\) to isolate \(x\):
\((x^3)^{\frac{1}{3}} = (3g-2h)^{\frac{1}{3}}\).
This simplifies to \(x = (3g-2h)^{\frac{1}{3}}\).

Therefore, the simplified expression is \((3g-2h)^{\frac{1}{3}}\), where \(x = (3g-2h)^{\frac{1}{3}}\).