\(a,2^n\cdot4=128\\ \Rightarrow2^n=32\\ \Rightarrow n=5\\ b,\Rightarrow\left(2^n+1\right)^3=5^3\\ \Rightarrow2^n+1=5\\ \Rightarrow2^n=4\Rightarrow n=2\\ c,n^{15}=n\\ \Rightarrow n^{15}-n=0\\ \Rightarrow n\left(n^{14}-1\right)=0\\ \Rightarrow\left[{}\begin{matrix}n=0\\n^{14}=1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}n=0\\n=1\\n=-1\end{matrix}\right.\)