Question

write the expression with only positive exponents and evaluate if possible: -2^{-3}
-2^{-3} = \square (simplify your answer. type an integer or a fraction.)

Explanation:

Step1: Recall negative exponent rule

The negative exponent rule states that \(a^{-n}=\frac{1}{a^{n}}\) for any non - zero number \(a\) and positive integer \(n\). For the expression \(-2^{-3}\), we first apply the negative exponent rule to the base \(2\) (note that the negative sign is not part of the base here, so we don't apply the rule to the negative sign). So \(2^{-3}=\frac{1}{2^{3}}\).

Step2: Calculate \(2^{3}\)

We know that \(2^{3}=2\times2\times2 = 8\).

Step3: Combine the results

Since \(2^{-3}=\frac{1}{2^{3}}=\frac{1}{8}\), then \(-2^{-3}=-\frac{1}{8}\).

Answer:

\(-\frac{1}{8}\)