Question

question
determine if the expression (-a^{-5}) is a polynomial or not. if it is a polynomial, state the type and degree of the polynomial.
answer
the given expression (\boldsymbol{-a^{-5}}) (\boldsymbol{\text{is not}}) a polynomial.

Explanation:

Step1: Rewrite the negative exponent

$ -a^{-5} = -\frac{1}{a^5} $

Step2: Check polynomial criteria

A polynomial consists of terms with non-negative integer exponents on variables. Here, the variable $a$ is in the denominator (equivalent to a negative exponent $-5$), which violates the definition of a polynomial.

Answer:

The expression $-a^{-5}$ is NOT a polynomial.