Final answer:
The expressions -x/3, 0, 1/3x, and x^3 are already in their simplest forms. Quadratic equations like x² + 0.0211x - 0.0211 = 0 can be solved using the quadratic formula. Other equations might require simplification or a different approach such as factoring or graphing to find the solution.
Step-by-step explanation:
The student's question seeks to simplify four different mathematical expressions: -x/3, 0, 1/3x, and x^3. Simplifying each of them requires different approaches:
- -x/3 is already in its simplest form.
- 0 is the additive identity and cannot be further simplified as it represents nothing or the absence of quantity.
- 1/3x is also in its simplest form, representing the quotient of one and three times x.
- For x^3, 'Cubing of Exponentials' states that one should cube the digit and multiply the exponent by 3, but since x has no exponent shown, it implies x is to the first power and so x^3 remains in its simplest form as is.
To address the various equations provided in the reference information:
- The equation x² + 0.0211x - 0.0211 = 0 is a quadratic equation, which can be solved using the quadratic formula or by factoring.
- The equation x² = 0.106 (0.360 - 1.202x + x²) needs to be expanded and simplified before attempting to solve it, and cannot be directly addressed with the quadratic formula as it eventually leads to a degree three equation.
- Expressions such as 3².35 require the application of exponent rules to simplify or evaluate the expression.
The student can solve these more complex equations through factoring, graphing, or applying the appropriate algebraic formula, as long as the equations are in the correct form.