One way to do it is by cleverly rewriting terms and using some basic algebraic identities:
[tex]4^n\cdot 2^{-18}=1[/tex].
[tex]2^{2n-18}=2^0[/tex].
[tex]2n-18=0[/tex].
[tex]n=18/2=\boxed{9}[/tex].
Another way would be to use logarithms, namely:
[tex]4^n\cdot2^{-18}=1\implies n=\log_4\Big({\frac{1}{2^{-18}}}\Big)=\boxed{9}[/tex].
Hope this helps.
