Question

rewrite the following without an exponent.
(-5)^{-3}

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 \( n \). For \( (-5)^{-3} \), we can apply this rule. So, \( (-5)^{-3}=\frac{1}{(-5)^{3}} \).

Step2: Calculate the denominator

We know that \( (-5)^{3}=(-5)\times(-5)\times(-5) \). First, \( (-5)\times(-5) = 25 \), then \( 25\times(-5)=- 125 \). So, \( \frac{1}{(-5)^{3}}=\frac{1}{-125}=-\frac{1}{125} \).

Answer:

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