Question

exponents and exponential functions
evaluating an expression with a negative exponent: negative integer base
rewrite the following without an exponent.
(-3)^{-1}

Explanation:

Step1: Recall 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). For \((-3)^{-1}\), we apply this rule.

Step2: Apply the rule

Using \(a = - 3\) and \(n = 1\) in the rule \(a^{-n}=\frac{1}{a^{n}}\), we get \((-3)^{-1}=\frac{1}{(-3)^{1}}\).

Step3: Simplify the denominator

Since \((-3)^{1}=-3\), the expression becomes \(\frac{1}{-3}\), which can be written as \(-\frac{1}{3}\).

Answer:

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