Sure! Let's simplify the given expression step by step:
1. Given Expression:
[tex]\[
x^3 + \frac{1}{x^3}
\][/tex]
2. First Term Analysis:
[tex]\[
x^3
\][/tex]
This term is already in its simplest form.
3. Second Term Analysis:
[tex]\[
\frac{1}{x^3}
\][/tex]
This term is also already in its simplest form.
4. Combining the Terms:
Since both terms are already simplified, we combine them to get the final expression:
[tex]\[
x^3 + \frac{1}{x^3}
\][/tex]
or equivalently,
[tex]\[
x^3 + x^{-3}
\][/tex]
since [tex]\( \frac{1}{x^3} \)[/tex] can be rewritten as [tex]\( x^{-3} \)[/tex].
So, the simplified result of the expression [tex]\( x^3 + \frac{1}{x^3} \)[/tex] is:
[tex]\[
x^3 + x^{-3}
\][/tex]
