Question

(-1).(-1)^2.(-1)^3.(-1)^4 ...(-1)^2010.(-1)^2011

Answer 1

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

Answer 2

\(\left(-1\right)\cdot\left(-1\right)^2\cdot\left(-1\right)^3\cdot...\cdot\left(-1\right)^{2010}\cdot\left(-1\right)^{2011}\)

\(=-1\cdot1\cdot1\cdot...\cdot1\)

=-1