Certainly! Let's simplify the expression [tex]\( x^{-12} \)[/tex].
1. Understand Negative Exponents:
The negative exponent rule states that [tex]\( x^{-a} = \frac{1}{x^a} \)[/tex]. This means any term with a negative exponent can be rewritten as a reciprocal with a positive exponent.
2. Apply the Rule:
Given the expression [tex]\( x^{-12} \)[/tex], we can apply the negative exponent rule:
[tex]\[
x^{-12} = \frac{1}{x^{12}}
\][/tex]
3. Review the Options:
We have the following options:
- [tex]\( x^{12} \)[/tex]
- [tex]\(-x^{12} \)[/tex]
- [tex]\( \frac{1}{x^{12}} \)[/tex]
- [tex]\(-\frac{1}{x^{12}} \)[/tex]
From our simplification [tex]\( x^{-12} = \frac{1}{x^{12}} \)[/tex].
4. Select the Correct Answer:
The correct simplified form of [tex]\( x^{-12} \)[/tex] is [tex]\(\frac{1}{x^{12}}\)[/tex].
Therefore, the simplified form is [tex]\(\frac{1}{x^{12}}\)[/tex].
