Question

evaluate:
$3^{-3}$

Explanation:

Step1: Recall the negative exponent rule

The rule for a negative exponent is \(a^{-n}=\frac{1}{a^{n}}\) (where \(a
eq0\) and \(n\) is a positive integer). So for \(3^{-3}\), we can rewrite it using this rule.
\(3^{-3}=\frac{1}{3^{3}}\)

Step2: Calculate \(3^{3}\)

We know that \(3^{3}=3\times3\times3 = 27\).

Step3: Substitute back

Substitute \(3^{3}=27\) into \(\frac{1}{3^{3}}\), we get \(\frac{1}{27}\).

Answer:

\(\frac{1}{27}\)