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.
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attempt 1 out of 2
the given expression (\boldsymbol{>}) a polynomial.
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Explanation:

Step1: Recall the definition of a polynomial

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

In the expression \( -a^{-5}\), we can rewrite it using the negative exponent rule \( a^{-n}=\frac{1}{a^n} \), so \( -a^{-5}=-\frac{1}{a^{5}} \). The exponent of \( a \) here is \(- 5\), which is a negative integer.

Step2: Conclusion about the expression

Since the exponent of the variable \( a \) in the expression \( -a^{-5} \) is a negative integer, the expression does not satisfy the definition of a polynomial.

Answer:

The given expression \(-a^{-5}\) is not a polynomial.