Question

1. simplify: $5^{-4}$

options: 625, -20, 1, $\frac{1}{625}$

Explanation:

Step1: Recall negative exponent rule

The rule for negative exponents is \( a^{-n}=\frac{1}{a^{n}} \) (where \( a
eq0 \) and \( n \) is a positive integer). For \( 5^{-4} \), we apply this rule, so \( 5^{-4}=\frac{1}{5^{4}} \).

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

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

Step3: Substitute back

Substituting \( 5^{4} = 625 \) into \( \frac{1}{5^{4}} \), we get \( \frac{1}{625} \).

Answer:

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