\(\left(-1\right)^{2n}\cdot\left(-1\right)^n\cdot\left(-1\right)^{n+1}\)
\(=\left(-1\right)^{2n+n+n+1}\)
\(=\left(-1\right)^{3n+1}\)
\(\left(-1\right)^{2n}.\left(-1\right)^n.\left(-1\right)^{n+1}=1^n.\left(-1\right)^n.\left(-1\right)^n.\left(-1\right)=1^n.1^n.\left(-1\right)=-1^n\)