Question

evaluate $5^{-4}$. 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 \(n\). For \(a = 5\) and \(n=4\), we have \(5^{-4}=\frac{1}{5^{4}}\).

Step2: Calculate \(5^{4}\)

We know that \(5^{4}=5\times5\times5\times5 = 625\).

Step3: Substitute the value of \(5^{4}\) into the fraction

Since \(5^{4} = 625\), then \(\frac{1}{5^{4}}=\frac{1}{625}\).

Answer:

\(\frac{1}{625}\)