Question

rewrite the following without an exponent.
$5^{-2}$

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 the expression \(5^{-2}\), here \(a = 5\) and \(n=2\). So we can rewrite \(5^{-2}\) as \(\frac{1}{5^{2}}\) according to the negative exponent rule.

Step2: Calculate the value of \(5^{2}\)

We know that \(5^{2}=5\times5 = 25\). So \(\frac{1}{5^{2}}=\frac{1}{25}\).

Answer:

\(\frac{1}{25}\)