Eliminating a Cubed Variable

An exponent represents how many times a number should be multiplied by itself. For example, ​x​3 (or x cubed) would be written out as ​x​ × ​x​ × ​x​. Canceling out a component in an equation requires using the opposite of that component. For example, subtracting 4 eliminates positive 4. The opposite of exponents are roots. The opposite of an exponent of 3 is a cubed root, indicated by this symbol: ³√.

1. Isolate the Cubed Variable

Isolate the instances of the cubed variable on one side of the equation. Practice using the example

(2x^3 + 2 = 3 – 6x^3)

First, add 6​x​3 to both sides. This leaves you with:

(8x^3 + 2 = 3)

Next, subtract 2 from both sides to isolate the variable:

(8x^3 = 1)

2. Eliminate the Coefficient

Eliminate the leading number or coefficient of the variable as the exponent only applies to the variable, not to that number. To continue the example, divide both sides of 8​x​3 = 1 by 8 to obtain

(x^3 = frac{1}{8})

3. Take the Cube Root

Eliminate the cube on the variable by taking the cube root of both sides of the equation:

(sqrt[3]{x^3}= sqrt[3]{frac{1}{8}} text{ or } x = sqrt[3]{frac{1}{8}})

Simplify the answer. Because the cube root of 8 is 2:

(sqrt[3]{frac{1}{8}} = frac{1}{2} text{ So }x = frac{1}{2})