Question

evaluate $(-2)^{-5}$. write your answer as a fraction in simplest form. the solution is \boxed{}.

Explanation:

Step1: Recall the negative exponent rule

The negative exponent rule states that \(a^{-n}=\frac{1}{a^{n}}\) for any non - zero real number \(a\) and positive integer \(n\). So, for \((-2)^{-5}\), we can rewrite it as \(\frac{1}{(-2)^{5}}\)

Step2: Calculate \((-2)^{5}\)

We know that \((-2)^{5}=(-2)\times(-2)\times(-2)\times(-2)\times(-2)\).
\((-2)\times(-2) = 4\), \(4\times(-2)=- 8\), \(-8\times(-2) = 16\), \(16\times(-2)=-32\)

Step3: Substitute the value of \((-2)^{5}\) into the fraction

Since \((-2)^{5}=-32\), then \(\frac{1}{(-2)^{5}}=\frac{1}{-32}=-\frac{1}{32}\)

Answer:

\(-\frac{1}{32}\)