Simplifying Cube Roots That Contain Variables

Next we will simplify a cube-root radical whose radicand contains a variable.

We will use a procedure similar to the one we used to simplify square-root radicals. However, when we simplify a cube-root radical, we divide the exponent of the variable by 3 (instead of 2).

Here are some examples.

If x is any real number, then:

In each example, the exponent of the variable in the simplified expression is one-third the exponent of the variable in the radicand.

Be careful:

If the power of x in the radicand is not a multiple of 3, we rewrite the radicand as a product where one of the factors has a power that is a multiple of 3 and the other factor is x¹ or x².

So,

 

Example

Simplify:

So,