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√.
Isolate the instances of the cubed variable on one side of the equation. Practice using the example 2x^3 + 2 = 3 - 6x^3. Add "6x^3" to both sides to get 8x^3 + 2 = 3. Subtract 2 from both sides to isolate the variable: 8x^3 = 1
Eliminate the leading number of the variable as the exponent only applies to the variable, not to that number. Divide both sides of 8x^3 = 1 by 8 to obtain x^3 = 1/8.
Eliminate the cube on the variable by taking the cube root of both sides of the equation: ³√(x^3) = ³√(1/8) or x = ³√(1/8). Simplify the answer. Because the cube root of 8 is 2, the cube root of 1/8 is 1/2. So x = 1/2.