Question

rewrite the following without an exponent.
(-5)^{-1}

Explanation:

Step1: Recall the negative exponent rule

The rule for a negative exponent is \(a^{-n}=\frac{1}{a^{n}}\) (where \(a
eq0\) and \(n\) is a positive integer). For \((-5)^{-1}\), here \(a = - 5\) and \(n=1\).

Step2: Apply the rule

Using the rule \(a^{-n}=\frac{1}{a^{n}}\), we substitute \(a=-5\) and \(n = 1\) into the formula. So \((-5)^{-1}=\frac{1}{(-5)^{1}}\).
Since \((-5)^{1}=-5\), then \(\frac{1}{(-5)^{1}}=\frac{1}{-5}=-\frac{1}{5}\).

Answer:

\(-\frac{1}{5}\)