Question

evaluate: $5^{-2} =$
a. $\frac{1}{25}$
b. $-25$
c. $\frac{1}{10}$
d. $-10$

Explanation:

Step1: Recall negative exponent rule

The rule for negative exponents is \( a^{-n} = \frac{1}{a^{n}} \) (where \( a
eq 0 \) and \( n \) is a positive integer). For \( 5^{-2} \), we apply this rule.

Step2: Apply the rule and simplify

Using the rule, \( 5^{-2}=\frac{1}{5^{2}} \). Since \( 5^{2}=5\times5 = 25 \), then \( \frac{1}{5^{2}}=\frac{1}{25} \).

Answer:

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