Question

simplify. express your answer as a single term, without a denomi
$s^{-1} \cdot s^{0}$

Explanation:

Step1: Apply exponent rule \(a^m \cdot a^n = a^{m + n}\)

For \(s^{-1} \cdot s^{0}\), we add the exponents: \(-1 + 0 = -1\), so it becomes \(s^{-1}\).

Step2: Apply negative exponent rule \(a^{-n}=\frac{1}{a^n}\) (but we need no denominator, so rewrite as \(a^{-n}=a^{n}\) in numerator? Wait, no: the negative exponent rule to eliminate denominator is \(a^{-n}=\frac{1}{a^n}\), but we need a single term without denominator. Wait, \(s^{-1}\) can be written as \(s^{-1}\) but maybe the problem means without negative exponents? Wait, the original problem says "without a denominator". Wait, \(s^{-1}=\frac{1}{s}\) has a denominator, but if we use exponent rules: first, \(s^0 = 1\) (any non - zero number to the power 0 is 1). Then \(s^{-1}\cdot1=s^{-1}\). But if we want to write it without a denominator (i.e., without a fraction), we can write it as \(s^{-1}\), but maybe the problem expects using the zero exponent rule first. Wait, \(s^0 = 1\), so \(s^{-1}\cdot s^0=s^{-1}\cdot1 = s^{-1}\). But maybe the problem wants to express it with a positive exponent? Wait, no, the problem says "without a denominator". Wait, \(s^{-1}\) is a single term without a denominator (it's a single term with a negative exponent). Wait, let's re - check the exponent rules.

First, recall that for any non - zero number \(a\), \(a^0 = 1\). So \(s^0=1\) (assuming \(s
eq0\)). Then, when multiplying two powers with the same base, we add the exponents: \(a^m\times a^n=a^{m + n}\). So for \(s^{-1}\times s^0\), we have \(m=-1\) and \(n = 0\), so \(s^{-1+0}=s^{-1}\).

Answer:

\(s^{-1}\) (or if we consider that maybe the problem wants positive exponent but without denominator, but \(s^{-1}\) is a single term without a denominator. Alternatively, if we made a mistake and the problem wants no negative exponents, but the problem says "without a denominator", and \(s^{-1}=\frac{1}{s}\) has a denominator, but \(s^{-1}\) as a term is without a denominator in the sense of a fraction. Wait, maybe the problem just wants the simplified form using exponent rules, so the answer is \(s^{-1}\) or \(s^{-1}\) which is \(s^{-1}\). But let's do it step by step:

Step 1: Use the zero - exponent property: \(s^0 = 1\) (for \(s
eq0\)).

Step 2: Multiply \(s^{-1}\) by \(s^0\): \(s^{-1}\times s^0=s^{-1}\times1=s^{-1}\).

So the simplified form is \(s^{-1}\).