Question

quiz
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expressions.
1 multiple choice 1 point
evaluate: $5^{-4}$
$\boldsymbol{-20}$
$\boldsymbol{20}$
$\boldsymbol{\frac{1}{625}}$
$\boldsymbol{-\frac{1}{625}}$
clear my selection
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Explanation:

Step1: Recall negative exponent rule

The rule for negative exponents is \( a^{-n} = \frac{1}{a^{n}} \) for any non - zero number \( a \) and positive integer \( n \). So for \( 5^{-4} \), we can rewrite it using this rule as \( \frac{1}{5^{4}} \).

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

We know that \( 5^{4}=5\times5\times5\times5 \). First, \( 5\times5 = 25 \), then \( 25\times5=125 \), and \( 125\times5 = 625 \).

Step3: Substitute back

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

Answer:

\(\frac{1}{625}\) (corresponding to the option \(\boldsymbol{\frac{1}{625}}\))