Question

what is the value of $3^{-1}$?
$3^{-1}=\square$

Explanation:

Step1: Recall the 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 \( 3^{-1} \), we apply this rule with \( a = 3 \) and \( n = 1 \).

Step2: Apply the rule to \( 3^{-1} \)

Using the rule \( a^{-n} = \frac{1}{a^{n}} \), we substitute \( a = 3 \) and \( n = 1 \) into the formula. So \( 3^{-1} = \frac{1}{3^{1}} \). Since \( 3^{1}=3 \), this simplifies to \( \frac{1}{3} \).

Answer:

\( \frac{1}{3} \)