Question

evaluate: \\((-5)^{-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 \((-5)^{-3}\), we can apply this rule.

Step2: Apply the rule and calculate the positive exponent

First, apply the negative exponent rule: \((-5)^{-3}=\frac{1}{(-5)^{3}}\). Then calculate \((-5)^{3}\), which is \((-5)\times(-5)\times(-5)= -125\).

Step3: Substitute the value back

Substitute \((-5)^{3}=-125\) into the fraction: \(\frac{1}{(-5)^{3}}=\frac{1}{-125}=-\frac{1}{125}\).

Answer:

\(-\frac{1}{125}\)