Question

simplify the following expression.
$(-4)^{-3}$
$(-4)^{-3}=\square$ (type an integer or a simplified fr

Explanation:

Step1: Recall negative exponent rule

The negative exponent rule states that \(a^{-n}=\frac{1}{a^{n}}\) for any non - zero real number \(a\) and positive integer \(n\). So, for \((-4)^{-3}\), we can rewrite it as \(\frac{1}{(-4)^{3}}\).

Step2: Calculate the denominator

Calculate \((-4)^{3}\). We know that \((-4)^{3}=(-4)\times(-4)\times(-4)\). First, \((-4)\times(-4) = 16\), then \(16\times(-4)=-64\). So, \((-4)^{3}=-64\).

Step3: Substitute the value of the denominator

Since \((-4)^{-3}=\frac{1}{(-4)^{3}}\) and \((-4)^{3}=-64\), then \((-4)^{-3}=\frac{1}{-64}=-\frac{1}{64}\).

Answer:

\(-\frac{1}{64}\)