\(\frac{1}{8}.16^n=2^n\)
\(\frac{1}{2^3}.\left(2^4\right)^n=2^n\)
\(\frac{1}{2^3}.2^{4n}=2^n\)
\(\frac{1}{2^3}=2^n:2^{4n}\)
\(\frac{1}{2^3}=2^{n-4n}\)
\(\frac{1}{2^3}=2^{n\left(1-4\right)}\)
\(\frac{1}{2^3}=2^{\left(-3\right)n}\)
\(2^{\left(-3\right)n}.2^3=1\)
\(2^{\left(-3\right)n+3}=1\)
\(2^{3\left(-n+1\right)}=2^0\)
\(\Rightarrow3\left(-n+1\right)=0\)
\(\Rightarrow-n+1=0\)
\(-n=-1\)
\(n=1\)
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