Question

question 15
simplify (2^{-3}).
select one
-8
8
1/8
-1/8

Explanation:

Step1: Recall negative exponent rule

The negative exponent rule states that \(a^{-n}=\frac{1}{a^{n}}\) for any non - zero number \(a\) and positive integer \(n\). For the expression \(2^{-3}\), here \(a = 2\) and \(n=3\). So we can rewrite \(2^{-3}\) as \(\frac{1}{2^{3}}\) according to the negative exponent rule.

Step2: Calculate \(2^{3}\)

We know that \(2^{3}=2\times2\times2 = 8\).

Step3: Substitute the value of \(2^{3}\)

Since \(2^{3}=8\), then \(\frac{1}{2^{3}}=\frac{1}{8}\).

Answer:

1/8