\(\left(-1\right).\left(-1\right)^2.\left(-1\right)^3.\left(-1\right)^4.....\left(-1\right)^{2010}.\left(-1\right)^{2011}.\)
\(=\left[\left(-1\right).\left(-1\right)^3.\left(-1\right)^5.....\left(-1\right)^{2011}\right].\left[\left(-1\right)^2.\left(-1\right)^4.\left(-1\right)^6.....\left(-1\right)^{2010}\right]\)
\(=1.1=1\)