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Friday 23rd of March
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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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# 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:

 since x Â· x Â· x = x3 since x4 Â· x4 Â· x4 = x12 Notice that since x9 Â· x9 Â· x9 = x27 Notice that

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.

 For example, letâ€™s simplify Write x14 as x12 Â· x2. Notice that 12 is a multiple of 3. Write as the product of two radicals. Simplify.

So,

Example

Simplify:

 Solution Factor the radicand, using perfect cube factors when possible. Write as a product of four radicals. Simplify the cube root of each perfect cube. Combine the remaining radicals.

So,