Final answer:
The polynomial in standard form is -7x^3 - (1/9)x - 1. It is already arranged in descending order, and no like terms need to be combined. Understanding algebraic principles and rules for exponents is important in simplification.
Step-by-step explanation:
To rewrite the polynomial -7x^3 - 1 - ⅓x in standard form, we should arrange the terms in descending order of their exponents and combine like terms if necessary. In this case, the polynomial is already in descending order with respect to the exponents of x. Therefore, the standard form is simply -7x^3 - ⅓x - 1, with the higher exponent term first, followed by the lower exponent term, and then the constant term.
When solving equations or simplifying expressions, it's important to follow algebraic principles such as eliminating terms wherever possible and checking the answer to ensure it is reasonable. Also, understanding that negative exponents denote a division rather than multiplication is crucial when dealing with expressions that contain them.