Question

question
determine if the expression (-a^{-3}) is a polynomial or not. if it is a polynomial, state the type and degree of the polynomial.
answer
the given expression (cdots) a polynomial.
represents
does not represent

Explanation:

Step1: Recall the definition of a polynomial

A polynomial in one variable \( x \) is an expression of the form \( a_nx^n + a_{n - 1}x^{n-1}+\cdots+a_1x + a_0 \), where \( n \) is a non - negative integer and \( a_i \) are real numbers. The exponents of the variable must be non - negative integers.

Step2: Analyze the given expression \(-a^{-3}\)

We can rewrite \(-a^{-3}\) using the negative exponent rule \( x^{-n}=\frac{1}{x^n} \). So, \(-a^{-3}=-\frac{1}{a^3}\). The exponent of \( a \) here is \(- 3\), which is a negative integer. Since the exponent of the variable in the expression \(-a^{-3}\) is not a non - negative integer, it does not satisfy the definition of a polynomial.

Answer:

The given expression \(\boldsymbol{\text{does NOT represent}}\) a polynomial.