Is this what you mean?:

x+\frac{1}{x}=2cos{\theta}, then

x^{6}+\frac{1}{x^{6}}=?

That is what you have written.

Unless you mean:

If \frac{x+1}{x}=2cos{\theta}, then

\frac{x^{6}+1}{x^{6}}=?

Just making sure.

By the way, why not use ^ (SHIFT 6) for a power instead of typing out 'power'?

And make use of brackets too to avoid confusion.