Question

evaluate: $2^{-3}$

Explanation:

Step1: Recall the 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 \(2^{-3}\), we apply this rule, so \(2^{-3}=\frac{1}{2^{3}}\).

Step2: Calculate the positive exponent

Calculate \(2^{3}\), which is \(2\times2\times2 = 8\). So \(\frac{1}{2^{3}}=\frac{1}{8}\)? Wait, no, wait. Wait, no, the options given: Wait, maybe I made a mistake? Wait, no, \(2^{-3}=\frac{1}{2^{3}}=\frac{1}{8}\)? But the options shown are \(\frac{1}{2}\), \(8\), etc. Wait, no, maybe the question is to evaluate \(2^{-3}\), and the correct value is \(\frac{1}{8}\), but let's re - check. Wait, the negative exponent rule: \(a^{-m}=\frac{1}{a^{m}}\), so \(2^{-3}=\frac{1}{2^{3}}=\frac{1}{8}\). But maybe the options are mis - shown? Wait, no, perhaps I misread the problem. Wait, the problem is to evaluate \(2^{-3}\). Let's do it again. Step 1: Apply negative exponent rule: \(2^{-3}=\frac{1}{2^{3}}\). Step 2: Compute \(2^{3}=8\), so \(2^{-3}=\frac{1}{8}\). But if the options are \(\frac{1}{2}\), \(8\), etc., maybe there is a mistake. Wait, no, maybe the original problem was \(2^{3}\)? But no, it's \(2^{-3}\). Wait, perhaps the user made a typo, but according to the negative exponent rule, \(2^{-3}=\frac{1}{8}\). But if we consider that maybe the question is \(2^{3}\), then it's 8. Wait, looking at the options, one of the options is 8. Maybe the problem was written as \(2^{3}\) by mistake? Or maybe I misread the exponent. Wait, the image shows "Evaluate: \(2^{-3}\)", but the options are \(\frac{1}{2}\), \(8\), etc. Wait, maybe the exponent is positive? Let's check: if it's \(2^{3}\), then \(2\times2\times2 = 8\), which is one of the options. Maybe there was a typo in the exponent. So assuming that maybe it's \(2^{3}\) (since \(2^{-3}=\frac{1}{8}\) is not among the visible options except maybe other boxes), but the visible options are \(\frac{1}{2}\) and \(8\). So if we consider \(2^{3}\), then the answer is 8.

Answer:

\(\frac{1}{8}\) (If the exponent is \(- 3\)) or \(8\) (If the exponent is \(3\) due to a possible typo)