Determine if the expression 3, a, to the power minus 53*a*−5 is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial.

Answer

Attempt 1 out of 2

The given expression  representsdoes NOT represent a polynomial.

Let's examine the given expression:

\[
3a^{-5} - 5
\]

### Step 1: Check if the expression is a polynomial
A polynomial is an algebraic expression consisting of variables and coefficients where the variables are raised to non-negative integer powers. The operations involved in forming a polynomial are addition, subtraction, and multiplication.

In the expression \(3a^{-5} - 5\), we have two terms:
1. \(3a^{-5}\) 
2. \(-5\)

The term \(3a^{-5}\) involves the variable \(a\) raised to the power of \(-5\). Since \(-5\) is a negative integer, this term violates the condition for being a polynomial (polynomials require non-negative integer exponents). 

### Step 2: Conclusion
Since the expression includes a term with a negative exponent (\(a^{-5}\)), it **does not** represent a polynomial.

### Final Answer:
The expression **does NOT** represent a polynomial.

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Would you like further details or have any questions? Here are some related questions you might consider:

1. What are the conditions for an algebraic expression to be a polynomial?
2. How do fractional or negative exponents affect the classification of an expression as a polynomial?
3. Can a polynomial have terms without a variable? If so, what are they called?
4. How do you identify the degree of a polynomial when all terms are valid?
5. What are some examples of expressions that look like polynomials but are not?

**Tip:** Always ensure that the exponents of variables in a polynomial are non-negative integers. This is key in determining if an expression qualifies as a polynomial.

Explore whether the expression 3a^-5 is a polynomial. Learn about polynomial definitions, including the requirement for non-negative integer exponents. Suitable for high school students studying algebra and polynomial functions.

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