Question

evaluate this expression
(-4)^{-3}
(-4)^{-3}=square
(type an integer or a simplified fraction.)

Explanation:

Step1: Recall the 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 \(n\). For the expression \((-4)^{-3}\), we can apply this rule. So, \((-4)^{-3}=\frac{1}{(-4)^{3}}\).

Step2: Calculate \((-4)^{3}\)

To calculate \((-4)^{3}\), we know that \((-4)^{3}=(-4)\times(-4)\times(-4)\). First, \((-4)\times(-4) = 16\), then \(16\times(-4)=-64\).

Step3: Substitute the value of \((-4)^{3}\) into the fraction

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

Answer:

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